Finite Groups of Order Less Than or Equal to 100 - LPSC

Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Finite Groups of Order Less Than or Equal to 100
This document contains additional material for the preprint:
K. Parattu, A. Wingerter, “Tribimaximal Mixing From Small Groups”, arXiv:1012.2842
In Tab. 1 below, we list the 1048 groups of order ≤ 100. The first column gives the GAP ID which
is a label that uniquely identifies the group in GAP. The first number in the square brackets is the
order of the group, and the second number simply enumerates different groups of the same order.
The second column gives the name of the group. If two or more groups by the same name are
isomorphic, we list only one. For the conventions we used in naming the groups and for a nonexhaustive
compilation of alternative names common in the physics and mathematics literature
see Appendix A of arXiv:1012.2842.
The third column indicates whether the group G has a 3-dimensional irreducible representation.
The fourth column indicates whether the group G is a subgroup of U(3). If G is in SU(3), an
orange check mark is shown (✔), otherwise a blue one (✔).
The fifth and sixth columns indicate whether G is in U(2) or U(2) × U(1), respectively (blue check
mark). If G is in SU(2) or SU(2) × U(1), respectively, the check mark is orange.
The seventh column indicates whether G contains A4 as a subgroup. The color of the check marks
has no significance.
Note that all Abelian groups are trivially contained in some Zp × Zq . . . × Zr, and the dashes (r)
indicate that we do not state whether they are subgroups of any U(n).
Table 1: The 1048 groups of order ≤ 100. For details, refer to the text preceding this table.
GAP ID Group 3 U3 U2 U2×1 A4
[1, 1] 1 ✗ r r r ✗
[2, 1] C2 ✗ r r r ✗
[3, 1] C3 ✗ r r r ✗
[4, 1] C4 ✗ r r r ✗
[4, 2] C2 × C2 ✗ r r r ✗
[5, 1] C5 ✗ r r r ✗
[6, 1] S3 ✗ ✔ ✔ ✔ ✗
[6, 2] C6 ✗ r r r ✗
[7, 1] C7 ✗ r r r ✗
[8, 1] C8 ✗ r r r ✗
[8, 2] C4 × C2 ✗ r r r ✗
[8, 3] D4 ✗ ✔ ✔ ✔ ✗
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GAP ID Group 3 U3 U2 U2×1 A4
[8, 4] Q8 ✗ ✔ ✔ ✔ ✗
[8, 5] C2 × C2 × C2 ✗ r r r ✗
[9, 1] C9 ✗ r r r ✗
[9, 2] C3 × C3 ✗ r r r ✗
[10, 1] D5 ✗ ✔ ✔ ✔ ✗
[10, 2] C10 ✗ r r r ✗
[11, 1] C11 ✗ r r r ✗
[12, 1] C3 ⋊ϕ C4 ✗ ✔ ✔ ✔ ✗
[12, 2] C12 ✗ r r r ✗
[12, 3] A4 ✔ ✔ ✗ ✗ ✔
[12, 4] D6 ✗ ✔ ✔ ✔ ✗
[12, 5] C6 × C2 ✗ r r r ✗
[13, 1] C13 ✗ r r r ✗
[14, 1] D7 ✗ ✔ ✔ ✔ ✗
[14, 2] C14 ✗ r r r ✗
[15, 1] C15 ✗ r r r ✗
[16, 1] C16 ✗ r r r ✗
[16, 2] C4 × C4 ✗ r r r ✗
[16, 3] (C4 × C2) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[16, 4] C4 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[16, 5] C8 × C2 ✗ r r r ✗
[16, 6] C8 ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[16, 7] D8 ✗ ✔ ✔ ✔ ✗
[16, 8] QD 8 ✗ ✔ ✔ ✔ ✗
[16, 9] Q16 ✗ ✔ ✔ ✔ ✗
[16, 10] C4 × C2 × C2 ✗ r r r ✗
[16, 11] C2 × D4 ✗ ✔ ✗ ✔ ✗
[16, 12] C2 × Q8 ✗ ✔ ✗ ✔ ✗
[16, 13] (C4 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[16, 14] C2 × C2 × C2 × C2 ✗ r r r ✗
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GAP ID Group 3 U3 U2 U2×1 A4
[17, 1] C17 ✗ r r r ✗
[18, 1] D9 ✗ ✔ ✔ ✔ ✗
[18, 2] C18 ✗ r r r ✗
[18, 3] C3 × S3 ✗ ✔ ✔ ✔ ✗
[18, 4] (C3 × C3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[18, 5] C6 × C3 ✗ r r r ✗
[19, 1] C19 ✗ r r r ✗
[20, 1] C5 ⋊ϕ C4 ✗ ✔ ✔ ✔ ✗
[20, 2] C20 ✗ r r r ✗
[20, 3] C5 ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[20, 4] D10 ✗ ✔ ✔ ✔ ✗
[20, 5] C10 × C2 ✗ r r r ✗
[21, 1] C7 ⋊ϕ C3 ✔ ✔ ✗ ✗ ✗
[21, 2] C21 ✗ r r r ✗
[22, 1] D11 ✗ ✔ ✔ ✔ ✗
[22, 2] C22 ✗ r r r ✗
[23, 1] C23 ✗ r r r ✗
[24, 1] C3 ⋊ϕ C8 ✗ ✔ ✔ ✔ ✗
[24, 2] C24 ✗ r r r ✗
[24, 3] SL(2, 3) ✔ ✔ ✔ ✔ ✗
[24, 4] C3 ⋊ϕ Q8 ✗ ✔ ✔ ✔ ✗
[24, 5] C4 × S3 ✗ ✔ ✔ ✔ ✗
[24, 6] D12 ✗ ✔ ✔ ✔ ✗
[24, 7] C2 × (C3 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[24, 8] (C6 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[24, 9] C12 × C2 ✗ r r r ✗
[24, 10] C3 × D4 ✗ ✔ ✔ ✔ ✗
[24, 11] C3 × Q8 ✗ ✔ ✔ ✔ ✗
[24, 12] S4 ✔ ✔ ✗ ✗ ✔
[24, 13] C2 × A4 ✔ ✔ ✗ ✗ ✔
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GAP ID Group 3 U3 U2 U2×1 A4
[24, 14] C2 × C2 × S3 ✗ ✔ ✗ ✔ ✗
[24, 15] C6 × C2 × C2 ✗ r r r ✗
[25, 1] C25 ✗ r r r ✗
[25, 2] C5 × C5 ✗ r r r ✗
[26, 1] D13 ✗ ✔ ✔ ✔ ✗
[26, 2] C26 ✗ r r r ✗
[27, 1] C27 ✗ r r r ✗
[27, 2] C9 × C3 ✗ r r r ✗
[27, 3] (C3 × C3) ⋊ϕ C3 ✔ ✔ ✗ ✗ ✗
[27, 4] C9 ⋊ϕ C3 ✔ ✔ ✗ ✗ ✗
[27, 5] C3 × C3 × C3 ✗ r r r ✗
[28, 1] C7 ⋊ϕ C4 ✗ ✔ ✔ ✔ ✗
[28, 2] C28 ✗ r r r ✗
[28, 3] D14 ✗ ✔ ✔ ✔ ✗
[28, 4] C14 × C2 ✗ r r r ✗
[29, 1] C29 ✗ r r r ✗
[30, 1] C5 × S3 ✗ ✔ ✔ ✔ ✗
[30, 2] C3 × D5 ✗ ✔ ✔ ✔ ✗
[30, 3] D15 ✗ ✔ ✔ ✔ ✗
[30, 4] C30 ✗ r r r ✗
[31, 1] C31 ✗ r r r ✗
[32, 1] C32 ✗ r r r ✗
[32, 2] (C4 × C2) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[32, 3] C8 × C4 ✗ r r r ✗
[32, 4] C8 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[32, 5] (C8 × C2) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[32, 6] ((C4 × C2) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 7] (C8 ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 8] (C2 × C2) → G → (C4 × C2) ✗ ✗ ✗ ✗ ✗
[32, 9] (C8 × C2) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
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GAP ID Group 3 U3 U2 U2×1 A4
[32, 10] Q8 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[32, 11] (C4 × C4) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[32, 12] C4 ⋊ϕ C8 ✗ ✔ ✗ ✔ ✗
[32, 13] C8 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[32, 14] C8 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[32, 15] C4 → G → (C4 × C2) ✗ ✔ ✔ ✔ ✗
[32, 16] C16 × C2 ✗ r r r ✗
[32, 17] C16 ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[32, 18] D16 ✗ ✔ ✔ ✔ ✗
[32, 19] QD 16 ✗ ✔ ✔ ✔ ✗
[32, 20] Q32 ✗ ✔ ✔ ✔ ✗
[32, 21] C4 × C4 × C2 ✗ r r r ✗
[32, 22] C2 × ((C4 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[32, 23] C2 × (C4 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[32, 24] (C4 × C4) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[32, 25] C4 × D4 ✗ ✔ ✗ ✔ ✗
[32, 26] C4 × Q8 ✗ ✔ ✗ ✔ ✗
[32, 27] (C2 × C2 × C2 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 28] (C4 × C2 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 29] (C2 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 30] (C4 × C2 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 31] (C4 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 32] (C2 × C2) → G → (C2 × C2 × C2) ✗ ✗ ✗ ✗ ✗
[32, 33] (C4 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 34] (C4 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 35] C4 ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[32, 36] C8 × C2 × C2 ✗ r r r ✗
[32, 37] C2 × (C8 ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[32, 38] (C8 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[32, 39] C2 × D8 ✗ ✔ ✗ ✔ ✗
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GAP ID Group 3 U3 U2 U2×1 A4
[32, 40] C2 × QD 8 ✗ ✔ ✗ ✔ ✗
[32, 41] C2 × Q16 ✗ ✔ ✗ ✔ ✗
[32, 42] (C8 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[32, 43] (C2 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 44] (C2 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 45] C4 × C2 × C2 × C2 ✗ r r r ✗
[32, 46] C2 × C2 × D4 ✗ ✗ ✗ ✗ ✗
[32, 47] C2 × C2 × Q8 ✗ ✗ ✗ ✗ ✗
[32, 48] C2 × ((C4 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[32, 49] (C2 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 50] (C2 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[32, 51] C2 × C2 × C2 × C2 × C2 ✗ r r r ✗
[33, 1] C33 ✗ r r r ✗
[34, 1] D17 ✗ ✔ ✔ ✔ ✗
[34, 2] C34 ✗ r r r ✗
[35, 1] C35 ✗ r r r ✗
[36, 1] C9 ⋊ϕ C4 ✗ ✔ ✔ ✔ ✗
[36, 2] C36 ✗ r r r ✗
[36, 3] (C2 × C2) ⋊ϕ C9 ✔ ✔ ✗ ✗ ✗
[36, 4] D18 ✗ ✔ ✔ ✔ ✗
[36, 5] C18 × C2 ✗ r r r ✗
[36, 6] C3 × (C3 ⋊ϕ C4) ✗ ✔ ✔ ✔ ✗
[36, 7] (C3 × C3) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[36, 8] C12 × C3 ✗ r r r ✗
[36, 9] (C3 × C3) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[36, 10] S3 × S3 ✗ ✗ ✗ ✗ ✗
[36, 11] C3 × A4 ✔ ✔ ✗ ✗ ✔
[36, 12] C6 × S3 ✗ ✔ ✔ ✔ ✗
[36, 13] C2 × ((C3 × C3) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[36, 14] C6 × C6 ✗ r r r ✗
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GAP ID Group 3 U3 U2 U2×1 A4
[37, 1] C37 ✗ r r r ✗
[38, 1] D19 ✗ ✔ ✔ ✔ ✗
[38, 2] C38 ✗ r r r ✗
[39, 1] C13 ⋊ϕ C3 ✔ ✔ ✗ ✗ ✗
[39, 2] C39 ✗ r r r ✗
[40, 1] C5 ⋊ϕ C8 ✗ ✔ ✔ ✔ ✗
[40, 2] C40 ✗ r r r ✗
[40, 3] C5 ⋊ϕ C8 ✗ ✗ ✗ ✗ ✗
[40, 4] C5 ⋊ϕ Q8 ✗ ✔ ✔ ✔ ✗
[40, 5] C4 × D5 ✗ ✔ ✔ ✔ ✗
[40, 6] D20 ✗ ✔ ✔ ✔ ✗
[40, 7] C2 × (C5 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[40, 8] (C10 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[40, 9] C20 × C2 ✗ r r r ✗
[40, 10] C5 × D4 ✗ ✔ ✔ ✔ ✗
[40, 11] C5 × Q8 ✗ ✔ ✔ ✔ ✗
[40, 12] C2 × (C5 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[40, 13] C2 × C2 × D5 ✗ ✔ ✗ ✔ ✗
[40, 14] C10 × C2 × C2 ✗ r r r ✗
[41, 1] C41 ✗ r r r ✗
[42, 1] (C7 ⋊ϕ C3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[42, 2] C2 × (C7 ⋊ϕ C3) ✔ ✔ ✗ ✗ ✗
[42, 3] C7 × S3 ✗ ✔ ✔ ✔ ✗
[42, 4] C3 × D7 ✗ ✔ ✔ ✔ ✗
[42, 5] D21 ✗ ✔ ✔ ✔ ✗
[42, 6] C42 ✗ r r r ✗
[43, 1] C43 ✗ r r r ✗
[44, 1] C11 ⋊ϕ C4 ✗ ✔ ✔ ✔ ✗
[44, 2] C44 ✗ r r r ✗
[44, 3] D22 ✗ ✔ ✔ ✔ ✗
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GAP ID Group 3 U3 U2 U2×1 A4
[44, 4] C22 × C2 ✗ r r r ✗
[45, 1] C45 ✗ r r r ✗
[45, 2] C15 × C3 ✗ r r r ✗
[46, 1] D23 ✗ ✔ ✔ ✔ ✗
[46, 2] C46 ✗ r r r ✗
[47, 1] C47 ✗ r r r ✗
[48, 1] C3 ⋊ϕ C16 ✗ ✔ ✔ ✔ ✗
[48, 2] C48 ✗ r r r ✗
[48, 3] (C4 × C4) ⋊ϕ C3 ✔ ✔ ✗ ✗ ✔
[48, 4] C8 × S3 ✗ ✔ ✔ ✔ ✗
[48, 5] C24 ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[48, 6] C24 ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[48, 7] D24 ✗ ✔ ✔ ✔ ✗
[48, 8] C3 ⋊ϕ Q16 ✗ ✔ ✔ ✔ ✗
[48, 9] C2 × (C3 ⋊ϕ C8) ✗ ✔ ✗ ✔ ✗
[48, 10] (C3 ⋊ϕ C8) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[48, 11] C4 × (C3 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[48, 12] (C3 ⋊ϕ C4) ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[48, 13] C12 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[48, 14] (C12 × C2) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[48, 15] (C3 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[48, 16] (C3 ⋊ϕ C8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[48, 17] (C3 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[48, 18] C3 ⋊ϕ Q16 ✗ ✗ ✗ ✗ ✗
[48, 19] (C2 × (C3 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[48, 20] C12 × C4 ✗ r r r ✗
[48, 21] C3 × ((C4 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[48, 22] C3 × (C4 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[48, 23] C24 × C2 ✗ r r r ✗
[48, 24] C3 × (C8 ⋊ϕ C2) ✗ ✔ ✔ ✔ ✗
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GAP ID Group 3 U3 U2 U2×1 A4
[48, 25] C3 × D8 ✗ ✔ ✔ ✔ ✗
[48, 26] C3 × QD 8 ✗ ✔ ✔ ✔ ✗
[48, 27] C3 × Q16 ✗ ✔ ✔ ✔ ✗
[48, 28] SL(2, 3) → G → C2 ✔ ✔ ✔ ✔ ✗
[48, 29] GL(2, 3) ✔ ✔ ✔ ✔ ✗
[48, 30] A4 ⋊ϕ C4 ✔ ✔ ✗ ✗ ✔
[48, 31] C4 × A4 ✔ ✔ ✗ ✗ ✔
[48, 32] C2 × SL(2, 3) ✔ ✔ ✗ ✔ ✗
[48, 33] SL(2, 3) ⋊ϕ C2 ✔ ✔ ✔ ✔ ✗
[48, 34] C2 × (C3 ⋊ϕ Q8) ✗ ✔ ✗ ✔ ✗
[48, 35] C2 × C4 × S3 ✗ ✔ ✗ ✔ ✗
[48, 36] C2 × D12 ✗ ✔ ✗ ✔ ✗
[48, 37] (C12 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[48, 38] D4 × S3 ✗ ✗ ✗ ✗ ✗
[48, 39] (C2 × (C3 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[48, 40] Q8 × S3 ✗ ✗ ✗ ✗ ✗
[48, 41] (C4 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[48, 42] C2 × C2 × (C3 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[48, 43] C2 × ((C6 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[48, 44] C12 × C2 × C2 ✗ r r r ✗
[48, 45] C6 × D4 ✗ ✔ ✗ ✔ ✗
[48, 46] C6 × Q8 ✗ ✔ ✗ ✔ ✗
[48, 47] C3 × ((C4 × C2) ⋊ϕ C2) ✗ ✔ ✔ ✔ ✗
[48, 48] C2 × S4 ✔ ✔ ✗ ✗ ✔
[48, 49] C2 × C2 × A4 ✔ ✗ ✗ ✗ ✔
[48, 50] (C2 × C2 × C2 × C2) ⋊ϕ C3 ✔ ✗ ✗ ✗ ✔
[48, 51] C2 × C2 × C2 × S3 ✗ ✗ ✗ ✗ ✗
[48, 52] C6 × C2 × C2 × C2 ✗ r r r ✗
[49, 1] C49 ✗ r r r ✗
[49, 2] C7 × C7 ✗ r r r ✗
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GAP ID Group 3 U3 U2 U2×1 A4
[50, 1] D25 ✗ ✔ ✔ ✔ ✗
[50, 2] C50 ✗ r r r ✗
[50, 3] C5 × D5 ✗ ✔ ✔ ✔ ✗
[50, 4] (C5 × C5) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[50, 5] C10 × C5 ✗ r r r ✗
[51, 1] C51 ✗ r r r ✗
[52, 1] C13 ⋊ϕ C4 ✗ ✔ ✔ ✔ ✗
[52, 2] C52 ✗ r r r ✗
[52, 3] C13 ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[52, 4] D26 ✗ ✔ ✔ ✔ ✗
[52, 5] C26 × C2 ✗ r r r ✗
[53, 1] C53 ✗ r r r ✗
[54, 1] D27 ✗ ✔ ✔ ✔ ✗
[54, 2] C54 ✗ r r r ✗
[54, 3] C3 × D9 ✗ ✔ ✔ ✔ ✗
[54, 4] C9 × S3 ✗ ✔ ✔ ✔ ✗
[54, 5] ((C3 × C3) ⋊ϕ C3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[54, 6] (C9 ⋊ϕ C3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[54, 7] (C9 × C3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[54, 8] ((C3 × C3) ⋊ϕ C3) ⋊ϕ C2 ✔ ✔ ✗ ✗ ✗
[54, 9] C18 × C3 ✗ r r r ✗
[54, 10] C2 × ((C3 × C3) ⋊ϕ C3) ✔ ✔ ✗ ✗ ✗
[54, 11] C2 × (C9 ⋊ϕ C3) ✔ ✔ ✗ ✗ ✗
[54, 12] C3 × C3 × S3 ✗ ✔ ✗ ✔ ✗
[54, 13] C3 × ((C3 × C3) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[54, 14] (C3 × C3 × C3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[54, 15] C6 × C3 × C3 ✗ r r r ✗
[55, 1] C11 ⋊ϕ C5 ✗ ✗ ✗ ✗ ✗
[55, 2] C55 ✗ r r r ✗
[56, 1] C7 ⋊ϕ C8 ✗ ✔ ✔ ✔ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[56, 2] C56 ✗ r r r ✗
[56, 3] C7 ⋊ϕ Q8 ✗ ✔ ✔ ✔ ✗
[56, 4] C4 × D7 ✗ ✔ ✔ ✔ ✗
[56, 5] D28 ✗ ✔ ✔ ✔ ✗
[56, 6] C2 × (C7 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[56, 7] (C14 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[56, 8] C28 × C2 ✗ r r r ✗
[56, 9] C7 × D4 ✗ ✔ ✔ ✔ ✗
[56, 10] C7 × Q8 ✗ ✔ ✔ ✔ ✗
[56, 11] (C2 × C2 × C2) ⋊ϕ C7 ✗ ✗ ✗ ✗ ✗
[56, 12] C2 × C2 × D7 ✗ ✔ ✗ ✔ ✗
[56, 13] C14 × C2 × C2 ✗ r r r ✗
[57, 1] C19 ⋊ϕ C3 ✔ ✔ ✗ ✗ ✗
[57, 2] C57 ✗ r r r ✗
[58, 1] D29 ✗ ✔ ✔ ✔ ✗
[58, 2] C58 ✗ r r r ✗
[59, 1] C59 ✗ r r r ✗
[60, 1] C5 × (C3 ⋊ϕ C4) ✗ ✔ ✔ ✔ ✗
[60, 2] C3 × (C5 ⋊ϕ C4) ✗ ✔ ✔ ✔ ✗
[60, 3] C15 ⋊ϕ C4 ✗ ✔ ✔ ✔ ✗
[60, 4] C60 ✗ r r r ✗
[60, 5] A5 ✔ ✔ ✗ ✗ ✔
[60, 6] C3 × (C5 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[60, 7] C15 ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[60, 8] S3 × D5 ✗ ✗ ✗ ✗ ✗
[60, 9] C5 × A4 ✔ ✔ ✗ ✗ ✔
[60, 10] C6 × D5 ✗ ✔ ✔ ✔ ✗
[60, 11] C10 × S3 ✗ ✔ ✔ ✔ ✗
[60, 12] D30 ✗ ✔ ✔ ✔ ✗
[60, 13] C30 × C2 ✗ r r r ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[61, 1] C61 ✗ r r r ✗
[62, 1] D31 ✗ ✔ ✔ ✔ ✗
[62, 2] C62 ✗ r r r ✗
[63, 1] C7 ⋊ϕ C9 ✔ ✔ ✗ ✗ ✗
[63, 2] C63 ✗ r r r ✗
[63, 3] C3 × (C7 ⋊ϕ C3) ✔ ✔ ✗ ✗ ✗
[63, 4] C21 × C3 ✗ r r r ✗
[64, 1] C64 ✗ r r r ✗
[64, 2] C8 × C8 ✗ r r r ✗
[64, 3] C8 ⋊ϕ C8 ✗ ✔ ✗ ✔ ✗
[64, 4] ((C8 × C2) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 5] (C4 × C2) ⋊ϕ C8 ✗ ✗ ✗ ✗ ✗
[64, 6] (C8 × C4) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[64, 7] Q8 ⋊ϕ C8 ✗ ✔ ✗ ✔ ✗
[64, 8] ((C8 × C2) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 9] (C2 × Q8) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 10] (C8 ⋊ϕ C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 11] (C4 × C2) → G → (C4 × C2) ✗ ✗ ✗ ✗ ✗
[64, 12] (C4 ⋊ϕ C8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 13] (C4 × C2) → G → (C4 × C2) ✗ ✗ ✗ ✗ ✗
[64, 14] (C4 × C2) → G → (C4 × C2) ✗ ✗ ✗ ✗ ✗
[64, 15] C8 ⋊ϕ C8 ✗ ✔ ✗ ✔ ✗
[64, 16] C8 ⋊ϕ C8 ✗ ✔ ✗ ✔ ✗
[64, 17] (C8 × C2) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 18] (C8 × C2) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 19] C4 → G → (C4 × C4) ✗ ✗ ✗ ✗ ✗
[64, 20] (C4 × C4) ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[64, 21] (C8 × C2) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 22] C4 → G → (C4 × C4) ✗ ✔ ✗ ✔ ✗
[64, 23] (C4 × C2 × C2) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[64, 24] (C8 ⋊ϕ C2) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 25] (C8 × C2) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 26] C16 × C4 ✗ r r r ✗
[64, 27] C16 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[64, 28] C16 ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 29] (C16 × C2) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[64, 30] (C16 ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 31] (C16 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[64, 32] ((C8 ⋊ϕ C2) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 33] (C4 × C2 × C2) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 34] (((C4 × C2) ⋊ϕ C2) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 35] (C4 × C4) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 36] (C2 × C2) → G → (C4 × C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 37] (C4 × C2) → G → (C4 × C2) ✗ ✗ ✗ ✗ ✗
[64, 38] (C16 × C2) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[64, 39] Q16 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[64, 40] (C16 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[64, 41] (C16 ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 42] (C16 ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 43] C8 → G → (C4 × C2) ✗ ✗ ✗ ✗ ✗
[64, 44] C4 ⋊ϕ C16 ✗ ✔ ✗ ✔ ✗
[64, 45] C4 → G → (C8 × C2) ✗ ✔ ✔ ✔ ✗
[64, 46] C16 ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 47] C16 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[64, 48] C16 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[64, 49] C8 → G → (C4 × C2) ✗ ✔ ✔ ✔ ✗
[64, 50] C32 × C2 ✗ r r r ✗
[64, 51] C32 ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[64, 52] D32 ✗ ✔ ✔ ✔ ✗
[64, 53] QD 32 ✗ ✔ ✔ ✔ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[64, 54] Q64 ✗ ✔ ✔ ✔ ✗
[64, 55] C4 × C4 × C4 ✗ r r r ✗
[64, 56] C2 × ((C4 × C2) ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[64, 57] (C4 × C4) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 58] C4 × ((C4 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 59] C4 × (C4 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[64, 60] (C2 × ((C4 × C2) ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 61] (C2 × (C4 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 62] ((C4 × C2) ⋊ϕ C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 63] (C4 × C4) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 64] (C4 × C4) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 65] (C4 × C4) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 66] (C2 × (C4 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 67] (C4 × C2 × C2 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 68] (C4 ⋊ϕ C4) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 69] (C4 × C4 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 70] (C4 ⋊ϕ C4) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 71] (C4 × C4 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 72] (C2 × Q8) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 73] (C2 × C2 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 74] (C2 × C2 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 75] (C2 × ((C4 × C2) ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 76] (C4 × C2) ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[64, 77] (C2 × (C4 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 78] (C2 × (C4 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 79] (C2 × C2 × C2) → G → (C2 × C2 × C2) ✗ ✗ ✗ ✗ ✗
[64, 80] (C2 × (C4 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 81] (C2 × C2 × C2) → G → (C2 × C2 × C2) ✗ ✗ ✗ ✗ ✗
[64, 82] (C2 × C2 × C2) → G → (C2 × C2 × C2) ✗ ✗ ✗ ✗ ✗
[64, 83] C8 × C4 × C2 ✗ r r r ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[64, 84] C2 × (C8 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[64, 85] C4 × (C8 ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[64, 86] (C8 × C4) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[64, 87] C2 × ((C8 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 88] (C2 × (C8 ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 89] (C8 × C2 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 90] C2 × (((C4 × C2) ⋊ϕ C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 91] (((C4 × C2) ⋊ϕ C2) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 92] C2 × ((C8 ⋊ϕ C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 93] (C2 × C2) → G → (C4 × C2)) ✗ ✗ ✗ ✗ ✗
[64, 94] (C2 × (C8 ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 95] C2 × ((C8 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 96] C2 × (Q8 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[64, 97] (C8 × C2 × C2) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[64, 98] (C2 × (C8 ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 99] (C2 × (C8 ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 100] (Q8 ⋊ϕ C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 101] C2 × ((C4 × C4) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[64, 102] (C2 × (C8 ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 103] C2 × (C4 ⋊ϕ C8) ✗ ✗ ✗ ✗ ✗
[64, 104] (C4 ⋊ϕ C8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 105] (C4 ⋊ϕ C8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 106] C2 × (C8 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[64, 107] C2 × (C8 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[64, 108] (C8 ⋊ϕ C4) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[64, 109] (C8 ⋊ϕ C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 110] C4 → G → (C4 × C2)) ✗ ✔ ✗ ✔ ✗
[64, 111] C4 → G → (C4 × C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 112] (C8 × C4) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[64, 113] (C4 ⋊ϕ C8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[64, 114] (C8 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 115] C8 × D4 ✗ ✔ ✗ ✔ ✗
[64, 116] (C8 × C2 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 117] (C8 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 118] C4 × D8 ✗ ✔ ✗ ✔ ✗
[64, 119] C4 × QD 8 ✗ ✔ ✗ ✔ ✗
[64, 120] C4 × Q16 ✗ ✔ ✗ ✔ ✗
[64, 121] (C4 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 122] Q16 ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[64, 123] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 124] (C8 × C4) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[64, 125] ((C4 × C4) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 126] C8 × Q8 ✗ ✔ ✗ ✔ ✗
[64, 127] C8 ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[64, 128] (C2 × C2 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 129] (C2 × C2 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 130] (C2 × D8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 131] (C2 × QD 8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 132] (C2 × Q16) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 133] (C2 × Q16) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 134] ((C4 × C4) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 135] ((C4 × C4) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 136] ((C4 × C4) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 137] ((C4 × C4) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 138] (((C4 × C2) ⋊ϕ C2) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 139] (((C4 × C2) ⋊ϕ C2) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 140] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 141] (C2 × QD 8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 142] (Q8 ⋊ϕ C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 143] C4 ⋊ϕ Q16 ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[64, 144] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 145] (C2 × Q16) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 146] (C8 × C2 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 147] (C8 × C2 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 148] (C2 × Q16) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 149] (C2 × (C8 ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 150] (C2 × (C8 ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 151] (C2 × Q16) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 152] (C2 × QD 8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 153] (C2 × D8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 154] (C2 × Q16) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 155] (C8 ⋊ϕ C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 156] Q8 ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[64, 157] (C8 ⋊ϕ C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 158] Q8 ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[64, 159] (C8 ⋊ϕ C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 160] (C4 × C2) → G → (C2 × C2 × C2) ✗ ✗ ✗ ✗ ✗
[64, 161] (C2 × (C4 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 162] (C2 × (C4 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 163] ((C8 × C2) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 164] (Q8 ⋊ϕ C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 165] (Q8 ⋊ϕ C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 166] (C8 ⋊ϕ C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 167] (C8 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 168] (C4 × C2) → G → (C2 × C2 × C2) ✗ ✗ ✗ ✗ ✗
[64, 169] (C8 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 170] (Q8 ⋊ϕ C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 171] ((C8 × C2) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 172] (C4 × C2) → G → (C2 × C2 × C2) ✗ ✗ ✗ ✗ ✗
[64, 173] (C8 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[64, 174] (C8 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 175] C4 ⋊ϕ Q16 ✗ ✗ ✗ ✗ ✗
[64, 176] (C8 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 177] (C2 × D8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 178] (C2 × Q16) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 179] C8 ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[64, 180] (C4 × C2) → G → (C2 × C2 × C2) ✗ ✗ ✗ ✗ ✗
[64, 181] C8 ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[64, 182] C8 ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[64, 183] C16 × C2 × C2 ✗ r r r ✗
[64, 184] C2 × (C16 ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[64, 185] (C16 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[64, 186] C2 × D16 ✗ ✔ ✗ ✔ ✗
[64, 187] C2 × QD 16 ✗ ✔ ✗ ✔ ✗
[64, 188] C2 × Q32 ✗ ✔ ✗ ✔ ✗
[64, 189] (C16 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[64, 190] (C2 × D8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 191] (C2 × Q16) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 192] C4 × C4 × C2 × C2 ✗ r r r ✗
[64, 193] C2 × C2 × ((C4 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 194] C2 × C2 × (C4 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[64, 195] C2 × ((C4 × C4) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 196] C2 × C4 × D4 ✗ ✗ ✗ ✗ ✗
[64, 197] C2 × C4 × Q8 ✗ ✗ ✗ ✗ ✗
[64, 198] C4 × ((C4 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[64, 199] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 200] (C4 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 201] (C4 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 202] C2 × ((C2 × C2 × C2 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 203] C2 × ((C4 × C2 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[64, 204] C2 × ((C2 × Q8) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 205] C2 × ((C4 × C2 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 206] (C4 × C2 × C2 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 207] C2 × ((C4 × C4) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 208] C2 × ((C2 × C2) → G → (C2 × C2 × C2)) ✗ ✗ ✗ ✗ ✗
[64, 209] C2 × ((C4 × C4) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 210] (C4 × C4 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 211] C2 × ((C4 × C4) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 212] C2 × (C4 ⋊ϕ Q8) ✗ ✗ ✗ ✗ ✗
[64, 213] (C4 × C4 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 214] (C4 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 215] (C2 × C2 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 216] (C2 × C2 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 217] (C2 × C2 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 218] (C2 × ((C4 × C2) ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 219] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 220] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 221] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 222] (C4 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 223] (C4 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 224] ((C2 × Q8) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 225] (C4 ⋊ϕ Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 226] D4 × D4 ✗ ✗ ✗ ✗ ✗
[64, 227] (C2 × C2 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 228] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 229] (C2 × C2 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 230] Q8 × D4 ✗ ✗ ✗ ✗ ✗
[64, 231] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 232] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 233] (C4 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[64, 234] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 235] (C4 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 236] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 237] (C4 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 238] Q8 ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[64, 239] Q8 × Q8 ✗ ✗ ✗ ✗ ✗
[64, 240] (C4 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 241] ((C4 × C2 × C2) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 242] ((C4 × C4) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 243] ((C2 × C2) → G → (C2 × C2 × C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 244] ((C4 × C4) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 245] (C2 × C2) → G → (C2 × C2 × C2 × C2) ✗ ✗ ✗ ✗ ✗
[64, 246] C8 × C2 × C2 × C2 ✗ r r r ✗
[64, 247] C2 × C2 × (C8 ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 248] C2 × ((C8 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[64, 249] (C2 × (C8 ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 250] C2 × C2 × D8 ✗ ✗ ✗ ✗ ✗
[64, 251] C2 × C2 × QD 8 ✗ ✗ ✗ ✗ ✗
[64, 252] C2 × C2 × Q16 ✗ ✗ ✗ ✗ ✗
[64, 253] C2 × ((C8 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[64, 254] C2 × ((C2 × D4) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 255] C2 × ((C2 × Q8) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 256] (C2 × (C8 ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 257] (C2 × D8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 258] (C2 × QD 8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 259] (C2 × Q16) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 260] C4 × C2 × C2 × C2 × C2 ✗ r r r ✗
[64, 261] C2 × C2 × C2 × D4 ✗ ✗ ✗ ✗ ✗
[64, 262] C2 × C2 × C2 × Q8 ✗ ✗ ✗ ✗ ✗
[64, 263] C2 × C2 × ((C4 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[64, 264] C2 × ((C2 × D4) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 265] C2 × ((C2 × Q8) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[64, 266] (C2 × ((C4 × C2) ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[64, 267] C2 × C2 × C2 × C2 × C2 × C2 ✗ r r r ✗
[65, 1] C65 ✗ r r r ✗
[66, 1] C11 × S3 ✗ ✔ ✔ ✔ ✗
[66, 2] C3 × D11 ✗ ✔ ✔ ✔ ✗
[66, 3] D33 ✗ ✔ ✔ ✔ ✗
[66, 4] C66 ✗ r r r ✗
[67, 1] C67 ✗ r r r ✗
[68, 1] C17 ⋊ϕ C4 ✗ ✔ ✔ ✔ ✗
[68, 2] C68 ✗ r r r ✗
[68, 3] C17 ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[68, 4] D34 ✗ ✔ ✔ ✔ ✗
[68, 5] C34 × C2 ✗ r r r ✗
[69, 1] C69 ✗ r r r ✗
[70, 1] C7 × D5 ✗ ✔ ✔ ✔ ✗
[70, 2] C5 × D7 ✗ ✔ ✔ ✔ ✗
[70, 3] D35 ✗ ✔ ✔ ✔ ✗
[70, 4] C70 ✗ r r r ✗
[71, 1] C71 ✗ r r r ✗
[72, 1] C9 ⋊ϕ C8 ✗ ✔ ✔ ✔ ✗
[72, 2] C72 ✗ r r r ✗
[72, 3] Q8 ⋊ϕ C9 ✔ ✔ ✔ ✔ ✗
[72, 4] C9 ⋊ϕ Q8 ✗ ✔ ✔ ✔ ✗
[72, 5] C4 × D9 ✗ ✔ ✔ ✔ ✗
[72, 6] D36 ✗ ✔ ✔ ✔ ✗
[72, 7] C2 × (C9 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[72, 8] (C18 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[72, 9] C36 × C2 ✗ r r r ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[72, 10] C9 × D4 ✗ ✔ ✔ ✔ ✗
[72, 11] C9 × Q8 ✗ ✔ ✔ ✔ ✗
[72, 12] C3 × (C3 ⋊ϕ C8) ✗ ✔ ✔ ✔ ✗
[72, 13] (C3 × C3) ⋊ϕ C8 ✗ ✗ ✗ ✗ ✗
[72, 14] C24 × C3 ✗ r r r ✗
[72, 15] ((C2 × C2) ⋊ϕ C9) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✗
[72, 16] C2 × ((C2 × C2) ⋊ϕ C9) ✔ ✔ ✗ ✗ ✗
[72, 17] C2 × C2 × D9 ✗ ✔ ✗ ✔ ✗
[72, 18] C18 × C2 × C2 ✗ r r r ✗
[72, 19] (C3 × C3) ⋊ϕ C8 ✗ ✗ ✗ ✗ ✗
[72, 20] (C3 ⋊ϕ C4) × S3 ✗ ✗ ✗ ✗ ✗
[72, 21] (C3 × (C3 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[72, 22] (C6 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[72, 23] (C6 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[72, 24] (C3 × C3) ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[72, 25] C3 × SL(2, 3) ✔ ✔ ✔ ✔ ✗
[72, 26] C3 × (C3 ⋊ϕ Q8) ✗ ✔ ✔ ✔ ✗
[72, 27] C12 × S3 ✗ ✔ ✔ ✔ ✗
[72, 28] C3 × D12 ✗ ✔ ✔ ✔ ✗
[72, 29] C6 × (C3 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[72, 30] C3 × ((C6 × C2) ⋊ϕ C2) ✗ ✔ ✔ ✔ ✗
[72, 31] (C3 × C3) ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[72, 32] C4 × ((C3 × C3) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[72, 33] (C12 × C3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[72, 34] C2 × ((C3 × C3) ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[72, 35] (C6 × C6) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[72, 36] C12 × C6 ✗ r r r ✗
[72, 37] C3 × C3 × D4 ✗ ✔ ✗ ✔ ✗
[72, 38] C3 × C3 × Q8 ✗ ✔ ✗ ✔ ✗
[72, 39] (C3 × C3) ⋊ϕ C8 ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[72, 40] (S3 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[72, 41] (C3 × C3) ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[72, 42] C3 × S4 ✔ ✔ ✗ ✗ ✔
[72, 43] (C3 × A4) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✔
[72, 44] A4 × S3 ✔ ✗ ✗ ✗ ✔
[72, 45] C2 × ((C3 × C3) ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[72, 46] C2 × S3 × S3 ✗ ✗ ✗ ✗ ✗
[72, 47] C6 × A4 ✔ ✔ ✗ ✗ ✔
[72, 48] C2 × C6 × S3 ✗ ✔ ✗ ✔ ✗
[72, 49] C2 × C2 × ((C3 × C3) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[72, 50] C6 × C6 × C2 ✗ r r r ✗
[73, 1] C73 ✗ r r r ✗
[74, 1] D37 ✗ ✔ ✔ ✔ ✗
[74, 2] C74 ✗ r r r ✗
[75, 1] C75 ✗ r r r ✗
[75, 2] (C5 × C5) ⋊ϕ C3 ✔ ✔ ✗ ✗ ✗
[75, 3] C15 × C5 ✗ r r r ✗
[76, 1] C19 ⋊ϕ C4 ✗ ✔ ✔ ✔ ✗
[76, 2] C76 ✗ r r r ✗
[76, 3] D38 ✗ ✔ ✔ ✔ ✗
[76, 4] C38 × C2 ✗ r r r ✗
[77, 1] C77 ✗ r r r ✗
[78, 1] (C13 ⋊ϕ C3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[78, 2] C2 × (C13 ⋊ϕ C3) ✔ ✔ ✗ ✗ ✗
[78, 3] C13 × S3 ✗ ✔ ✔ ✔ ✗
[78, 4] C3 × D13 ✗ ✔ ✔ ✔ ✗
[78, 5] D39 ✗ ✔ ✔ ✔ ✗
[78, 6] C78 ✗ r r r ✗
[79, 1] C79 ✗ r r r ✗
[80, 1] C5 ⋊ϕ C16 ✗ ✔ ✔ ✔ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[80, 2] C80 ✗ r r r ✗
[80, 3] C5 ⋊ϕ C16 ✗ ✗ ✗ ✗ ✗
[80, 4] C8 × D5 ✗ ✔ ✔ ✔ ✗
[80, 5] C40 ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[80, 6] C40 ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[80, 7] D40 ✗ ✔ ✔ ✔ ✗
[80, 8] C5 ⋊ϕ Q16 ✗ ✔ ✔ ✔ ✗
[80, 9] C2 × (C5 ⋊ϕ C8) ✗ ✔ ✗ ✔ ✗
[80, 10] (C5 ⋊ϕ C8) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[80, 11] C4 × (C5 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[80, 12] (C5 ⋊ϕ C4) ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[80, 13] C20 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[80, 14] (C20 × C2) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[80, 15] (C5 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[80, 16] (C5 ⋊ϕ C8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[80, 17] (C5 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[80, 18] C5 ⋊ϕ Q16 ✗ ✗ ✗ ✗ ✗
[80, 19] (C2 × (C5 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[80, 20] C20 × C4 ✗ r r r ✗
[80, 21] C5 × ((C4 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[80, 22] C5 × (C4 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[80, 23] C40 × C2 ✗ r r r ✗
[80, 24] C5 × (C8 ⋊ϕ C2) ✗ ✔ ✔ ✔ ✗
[80, 25] C5 × D8 ✗ ✔ ✔ ✔ ✗
[80, 26] C5 × QD 8 ✗ ✔ ✔ ✔ ✗
[80, 27] C5 × Q16 ✗ ✔ ✔ ✔ ✗
[80, 28] (C5 ⋊ϕ C8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[80, 29] (C5 ⋊ϕ C8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[80, 30] C4 × (C5 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[80, 31] C20 ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[80, 32] C2 × (C5 ⋊ϕ C8) ✗ ✗ ✗ ✗ ✗
[80, 33] (C5 ⋊ϕ C8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[80, 34] (C2 × (C5 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[80, 35] C2 × (C5 ⋊ϕ Q8) ✗ ✔ ✗ ✔ ✗
[80, 36] C2 × C4 × D5 ✗ ✔ ✗ ✔ ✗
[80, 37] C2 × D20 ✗ ✔ ✗ ✔ ✗
[80, 38] (C20 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[80, 39] D4 × D5 ✗ ✗ ✗ ✗ ✗
[80, 40] (C2 × (C5 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[80, 41] Q8 × D5 ✗ ✗ ✗ ✗ ✗
[80, 42] (C4 × D5) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[80, 43] C2 × C2 × (C5 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[80, 44] C2 × ((C10 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[80, 45] C20 × C2 × C2 ✗ r r r ✗
[80, 46] C10 × D4 ✗ ✔ ✗ ✔ ✗
[80, 47] C10 × Q8 ✗ ✔ ✗ ✔ ✗
[80, 48] C5 × ((C4 × C2) ⋊ϕ C2) ✗ ✔ ✔ ✔ ✗
[80, 49] (C2 × C2 × C2 × C2) ⋊ϕ C5 ✗ ✗ ✗ ✗ ✗
[80, 50] C2 × C2 × (C5 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[80, 51] C2 × C2 × C2 × D5 ✗ ✗ ✗ ✗ ✗
[80, 52] C10 × C2 × C2 × C2 ✗ r r r ✗
[81, 1] C81 ✗ r r r ✗
[81, 2] C9 × C9 ✗ r r r ✗
[81, 3] (C9 × C3) ⋊ϕ C3 ✔ ✗ ✗ ✗ ✗
[81, 4] C9 ⋊ϕ C9 ✔ ✗ ✗ ✗ ✗
[81, 5] C27 × C3 ✗ r r r ✗
[81, 6] C27 ⋊ϕ C3 ✔ ✔ ✗ ✗ ✗
[81, 7] (C3 × C3 × C3) ⋊ϕ C3 ✔ ✔ ✗ ✗ ✗
[81, 8] (C9 × C3) ⋊ϕ C3 ✔ ✔ ✗ ✗ ✗
[81, 9] (C9 × C3) ⋊ϕ C3 ✔ ✔ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[81, 10] (C3 × C3) → G → (C3 × C3) ✔ ✔ ✗ ✗ ✗
[81, 11] C9 × C3 × C3 ✗ r r r ✗
[81, 12] C3 × ((C3 × C3) ⋊ϕ C3) ✔ ✗ ✗ ✗ ✗
[81, 13] C3 × (C9 ⋊ϕ C3) ✔ ✗ ✗ ✗ ✗
[81, 14] (C9 × C3) ⋊ϕ C3 ✔ ✔ ✗ ✗ ✗
[81, 15] C3 × C3 × C3 × C3 ✗ r r r ✗
[82, 1] D41 ✗ ✔ ✔ ✔ ✗
[82, 2] C82 ✗ r r r ✗
[83, 1] C83 ✗ r r r ✗
[84, 1] (C7 ⋊ϕ C4) ⋊ϕ C3 ✗ ✗ ✗ ✗ ✗
[84, 2] C4 × (C7 ⋊ϕ C3) ✔ ✔ ✗ ✗ ✗
[84, 3] C7 × (C3 ⋊ϕ C4) ✗ ✔ ✔ ✔ ✗
[84, 4] C3 × (C7 ⋊ϕ C4) ✗ ✔ ✔ ✔ ✗
[84, 5] C21 ⋊ϕ C4 ✗ ✔ ✔ ✔ ✗
[84, 6] C84 ✗ r r r ✗
[84, 7] C2 × ((C7 ⋊ϕ C3) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[84, 8] S3 × D7 ✗ ✗ ✗ ✗ ✗
[84, 9] C2 × C2 × (C7 ⋊ϕ C3) ✔ ✗ ✗ ✗ ✗
[84, 10] C7 × A4 ✔ ✔ ✗ ✗ ✔
[84, 11] (C14 × C2) ⋊ϕ C3 ✔ ✔ ✗ ✗ ✔
[84, 12] C6 × D7 ✗ ✔ ✔ ✔ ✗
[84, 13] C14 × S3 ✗ ✔ ✔ ✔ ✗
[84, 14] D42 ✗ ✔ ✔ ✔ ✗
[84, 15] C42 × C2 ✗ r r r ✗
[85, 1] C85 ✗ r r r ✗
[86, 1] D43 ✗ ✔ ✔ ✔ ✗
[86, 2] C86 ✗ r r r ✗
[87, 1] C87 ✗ r r r ✗
[88, 1] C11 ⋊ϕ C8 ✗ ✔ ✔ ✔ ✗
[88, 2] C88 ✗ r r r ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[88, 3] C11 ⋊ϕ Q8 ✗ ✔ ✔ ✔ ✗
[88, 4] C4 × D11 ✗ ✔ ✔ ✔ ✗
[88, 5] D44 ✗ ✔ ✔ ✔ ✗
[88, 6] C2 × (C11 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[88, 7] (C22 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[88, 8] C44 × C2 ✗ r r r ✗
[88, 9] C11 × D4 ✗ ✔ ✔ ✔ ✗
[88, 10] C11 × Q8 ✗ ✔ ✔ ✔ ✗
[88, 11] C2 × C2 × D11 ✗ ✔ ✗ ✔ ✗
[88, 12] C22 × C2 × C2 ✗ r r r ✗
[89, 1] C89 ✗ r r r ✗
[90, 1] C5 × D9 ✗ ✔ ✔ ✔ ✗
[90, 2] C9 × D5 ✗ ✔ ✔ ✔ ✗
[90, 3] D45 ✗ ✔ ✔ ✔ ✗
[90, 4] C90 ✗ r r r ✗
[90, 5] C3 × C3 × D5 ✗ ✔ ✗ ✔ ✗
[90, 6] C15 × S3 ✗ ✔ ✔ ✔ ✗
[90, 7] C3 × D15 ✗ ✔ ✔ ✔ ✗
[90, 8] C5 × ((C3 × C3) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[90, 9] (C15 × C3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[90, 10] C30 × C3 ✗ r r r ✗
[91, 1] C91 ✗ r r r ✗
[92, 1] C23 ⋊ϕ C4 ✗ ✔ ✔ ✔ ✗
[92, 2] C92 ✗ r r r ✗
[92, 3] D46 ✗ ✔ ✔ ✔ ✗
[92, 4] C46 × C2 ✗ r r r ✗
[93, 1] C31 ⋊ϕ C3 ✔ ✔ ✗ ✗ ✗
[93, 2] C93 ✗ r r r ✗
[94, 1] D47 ✗ ✔ ✔ ✔ ✗
[94, 2] C94 ✗ r r r ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[95, 1] C95 ✗ r r r ✗
[96, 1] C3 ⋊ϕ C32 ✗ ✔ ✔ ✔ ✗
[96, 2] C96 ✗ r r r ✗
[96, 3] ((C4 × C2) ⋊ϕ C4) ⋊ϕ C3 ✔ ✗ ✗ ✗ ✔
[96, 4] C16 × S3 ✗ ✔ ✔ ✔ ✗
[96, 5] C48 ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[96, 6] D48 ✗ ✔ ✔ ✔ ✗
[96, 7] C48 ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[96, 8] C3 ⋊ϕ Q32 ✗ ✔ ✔ ✔ ✗
[96, 9] C4 × (C3 ⋊ϕ C8) ✗ ✔ ✗ ✔ ✗
[96, 10] (C3 ⋊ϕ C8) ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[96, 11] C12 ⋊ϕ C8 ✗ ✔ ✗ ✔ ✗
[96, 12] (C12 × C4) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[96, 13] (C3 × ((C4 × C2) ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 14] (C3 ⋊ϕ C8) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[96, 15] (C3 ⋊ϕ C8) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[96, 16] (C2 × (C3 ⋊ϕ C8)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 17] (C3 ⋊ϕ Q8) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[96, 18] C2 × (C3 ⋊ϕ C16) ✗ ✔ ✗ ✔ ✗
[96, 19] (C3 ⋊ϕ C16) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[96, 20] C8 × (C3 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[96, 21] (C3 ⋊ϕ C4) ⋊ϕ C8 ✗ ✔ ✗ ✔ ✗
[96, 22] C24 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[96, 23] (C3 ⋊ϕ Q8) ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[96, 24] C24 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[96, 25] C24 ⋊ϕ C4 ✗ ✔ ✗ ✔ ✗
[96, 26] C4 → G → (C4 × C2)) ✗ ✔ ✔ ✔ ✗
[96, 27] (C24 × C2) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[96, 28] (C24 × C2) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[96, 29] C4 → G → (C4 × C2)) ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[96, 30] (C3 × (C8 ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 31] (C2 × C2) → G → (C4 × C2)) ✗ ✗ ✗ ✗ ✗
[96, 32] (C3 × (C8 ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 33] (C3 × D8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 34] (C3 ⋊ϕ C16) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 35] (C3 × Q16) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 36] C3 ⋊ϕ Q32 ✗ ✗ ✗ ✗ ✗
[96, 37] (C2 × (C3 ⋊ϕ C8)) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[96, 38] (C12 × C2) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[96, 39] (C2 × (C3 ⋊ϕ C8)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 40] ((C3 ⋊ϕ C8) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 41] ((C2 × (C3 ⋊ϕ C4)) ⋊ϕ C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 42] (C3 × Q8) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[96, 43] (C2 × C2) → G → (C4 × C2)) ✗ ✗ ✗ ✗ ✗
[96, 44] (C4 × (C3 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 45] C3 × ((C4 × C2) ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[96, 46] C24 × C4 ✗ r r r ✗
[96, 47] C3 × (C8 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[96, 48] C3 × ((C8 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[96, 49] C3 × (((C4 × C2) ⋊ϕ C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 50] C3 × ((C8 ⋊ϕ C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 51] (C2 × C2) → G → (C4 × C2)) ✗ ✗ ✗ ✗ ✗
[96, 52] C3 × ((C8 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[96, 53] C3 × (Q8 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[96, 54] C3 × ((C4 × C4) ⋊ϕ C2) ✗ ✔ ✔ ✔ ✗
[96, 55] C3 × (C4 ⋊ϕ C8) ✗ ✔ ✗ ✔ ✗
[96, 56] C3 × (C8 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[96, 57] C3 × (C8 ⋊ϕ C4) ✗ ✔ ✗ ✔ ✗
[96, 58] C4 → G → (C4 × C2)) ✗ ✔ ✔ ✔ ✗
[96, 59] C48 × C2 ✗ r r r ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[96, 60] C3 × (C16 ⋊ϕ C2) ✗ ✔ ✔ ✔ ✗
[96, 61] C3 × D16 ✗ ✔ ✔ ✔ ✗
[96, 62] C3 × QD 16 ✗ ✔ ✔ ✔ ✗
[96, 63] C3 × Q32 ✗ ✔ ✔ ✔ ✗
[96, 64] ((C4 × C4) ⋊ϕ C3) ⋊ϕ C2 ✔ ✔ ✗ ✗ ✔
[96, 65] A4 ⋊ϕ C8 ✔ ✔ ✗ ✗ ✔
[96, 66] SL(2, 3) ⋊ϕ C4 ✔ ✔ ✗ ✔ ✗
[96, 67] SL(2, 3) ⋊ϕ C4 ✔ ✔ ✔ ✔ ✗
[96, 68] C2 × ((C4 × C4) ⋊ϕ C3) ✔ ✔ ✗ ✗ ✔
[96, 69] C4 × SL(2, 3) ✔ ✔ ✗ ✔ ✗
[96, 70] ((C2 × C2 × C2 × C2) ⋊ϕ C3) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✔
[96, 71] ((C4 × C4) ⋊ϕ C3) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✔
[96, 72] ((C4 × C4) ⋊ϕ C3) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✔
[96, 73] C8 × A4 ✔ ✔ ✗ ✗ ✔
[96, 74] ((C8 × C2) ⋊ϕ C2) ⋊ϕ C3 ✔ ✔ ✔ ✔ ✗
[96, 75] C4 × (C3 ⋊ϕ Q8) ✗ ✔ ✗ ✔ ✗
[96, 76] C12 ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[96, 77] C3 ⋊ϕ ((C2 × C2) → G → (C2 × C2 × C2)) ✗ ✗ ✗ ✗ ✗
[96, 78] C4 × C4 × S3 ✗ ✔ ✗ ✔ ✗
[96, 79] (C12 × C4) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[96, 80] C4 × D12 ✗ ✔ ✗ ✔ ✗
[96, 81] (C12 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 82] (C12 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 83] (C12 × C4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 84] (C4 × (C3 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 85] (C2 × (C3 ⋊ϕ Q8)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 86] (C4 × (C3 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 87] ((C4 × C2) ⋊ϕ C2) × S3 ✗ ✗ ✗ ✗ ✗
[96, 88] (C2 × C4 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 89] (C2 × C2 × C2 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[96, 90] (C2 × C4 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 91] (C2 × C4 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 92] (C2 × (C3 ⋊ϕ Q8)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 93] (C2 × C2 × (C3 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 94] (C3 ⋊ϕ Q8) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[96, 95] C12 ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[96, 96] C3 ⋊ϕ ((C2 × C2) → G → (C2 × C2 × C2)) ✗ ✗ ✗ ✗ ✗
[96, 97] C3 ⋊ϕ ((C2 × C2) → G → (C2 × C2 × C2)) ✗ ✗ ✗ ✗ ✗
[96, 98] (C4 ⋊ϕ C4) × S3 ✗ ✗ ✗ ✗ ✗
[96, 99] (C4 × (C3 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 100] (C2 × C4 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 101] (C2 × C4 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 102] (C2 × C4 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 103] (C2 × (C3 ⋊ϕ Q8)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 104] (C3 × (C4 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 105] (C3 × (C4 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 106] C2 × C8 × S3 ✗ ✔ ✗ ✔ ✗
[96, 107] C2 × (C24 ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[96, 108] (C24 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[96, 109] C2 × (C24 ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[96, 110] C2 × D24 ✗ ✔ ✗ ✔ ✗
[96, 111] (C24 × C2) ⋊ϕ C2 ✗ ✔ ✔ ✔ ✗
[96, 112] C2 × (C3 ⋊ϕ Q16) ✗ ✔ ✗ ✔ ✗
[96, 113] (C8 ⋊ϕ C2) × S3 ✗ ✗ ✗ ✗ ✗
[96, 114] (C8 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 115] (C2 × D12) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 116] (C3 × (C8 ⋊ϕ C2)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 117] D8 × S3 ✗ ✗ ✗ ✗ ✗
[96, 118] (D4 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 119] (C8 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[96, 120] QD 8 × S3 ✗ ✗ ✗ ✗ ✗
[96, 121] (D4 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 122] (Q8 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 123] (C8 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 124] Q16 × S3 ✗ ✗ ✗ ✗ ✗
[96, 125] (C3 × Q16) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 126] (C8 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 127] C2 × C2 × (C3 ⋊ϕ C8) ✗ ✗ ✗ ✗ ✗
[96, 128] C2 × ((C3 ⋊ϕ C8) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[96, 129] C2 × C4 × (C3 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[96, 130] C2 × ((C3 ⋊ϕ C4) ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[96, 131] (C2 × (C3 ⋊ϕ Q8)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 132] C2 × (C12 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[96, 133] (C4 × (C3 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✔ ✗ ✔ ✗
[96, 134] C2 × ((C12 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 135] C4 × ((C6 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[96, 136] (C12 × C2 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 137] (C12 × C2 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 138] C2 × ((C3 × D4) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 139] (C6 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 140] C2 × ((C3 ⋊ϕ C8) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 141] D4 × (C3 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[96, 142] (C2 × C2 × (C3 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 143] (C2 × (C3 ⋊ϕ Q8)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 144] (C2 × C2 × C2 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 145] (C6 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 146] (C2 × C2 × (C3 ⋊ϕ C4)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 147] (C6 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 148] C2 × ((C3 × Q8) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 149] (C6 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[96, 150] C2 × (C3 ⋊ϕ Q16) ✗ ✗ ✗ ✗ ✗
[96, 151] (C3 ⋊ϕ C4) ⋊ϕ Q8 ✗ ✗ ✗ ✗ ✗
[96, 152] Q8 × (C3 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[96, 153] (C6 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 154] (C6 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 155] (C2 × (C3 ⋊ϕ C8)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 156] (C2 × D12) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 157] (C2 × (C3 ⋊ϕ C8)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 158] (C2 × (C3 ⋊ϕ Q8)) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 159] C2 × ((C2 × (C3 ⋊ϕ C4)) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 160] (C6 × C2 × C2 × C2) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 161] C12 × C4 × C2 ✗ r r r ✗
[96, 162] C6 × ((C4 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 163] C6 × (C4 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[96, 164] C3 × ((C4 × C4) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[96, 165] C12 × D4 ✗ ✔ ✗ ✔ ✗
[96, 166] C12 × Q8 ✗ ✔ ✗ ✔ ✗
[96, 167] C3 × ((C2 × C2 × C2 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 168] C3 × ((C4 × C2 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 169] C3 × ((C2 × Q8) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 170] C3 × ((C4 × C2 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 171] C3 × ((C4 × C4) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 172] C3 × ((C2 × C2) → G → (C2 × C2 × C2)) ✗ ✗ ✗ ✗ ✗
[96, 173] C3 × ((C4 × C4) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 174] C3 × ((C4 × C4) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 175] C3 × (C4 ⋊ϕ Q8) ✗ ✗ ✗ ✗ ✗
[96, 176] C24 × C2 × C2 ✗ r r r ✗
[96, 177] C6 × (C8 ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[96, 178] C3 × ((C8 × C2) ⋊ϕ C2) ✗ ✔ ✔ ✔ ✗
[96, 179] C6 × D8 ✗ ✔ ✗ ✔ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[96, 180] C6 × QD 8 ✗ ✔ ✗ ✔ ✗
[96, 181] C6 × Q16 ✗ ✔ ✗ ✔ ✗
[96, 182] C3 × ((C8 × C2) ⋊ϕ C2) ✗ ✔ ✔ ✔ ✗
[96, 183] C3 × ((C2 × D4) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 184] C3 × ((C2 × Q8) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 185] A4 ⋊ϕ Q8 ✔ ✗ ✗ ✗ ✔
[96, 186] C4 × S4 ✔ ✔ ✗ ✗ ✔
[96, 187] (C2 × S4) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✔
[96, 188] SL(2, 3) → G → C2) ✔ ✔ ✗ ✔ ✗
[96, 189] C2 × GL(2, 3) ✔ ✔ ✗ ✔ ✗
[96, 190] (C2 × SL(2, 3)) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✗
[96, 191] SL(2, 3) → G → C2) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✗
[96, 192] SL(2, 3) → G → C2) ⋊ϕ C2 ✔ ✔ ✔ ✔ ✗
[96, 193] (SL(2, 3) ⋊ϕ C2) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✗
[96, 194] C2 × (A4 ⋊ϕ C4) ✔ ✗ ✗ ✗ ✔
[96, 195] (C2 × C2 × A4) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✔
[96, 196] C2 × C4 × A4 ✔ ✗ ✗ ✗ ✔
[96, 197] D4 × A4 ✔ ✗ ✗ ✗ ✔
[96, 198] C2 × C2 × SL(2, 3) ✔ ✗ ✗ ✗ ✗
[96, 199] Q8 × A4 ✔ ✗ ✗ ✗ ✔
[96, 200] C2 × (SL(2, 3) ⋊ϕ C2) ✔ ✔ ✗ ✔ ✗
[96, 201] (SL(2, 3) ⋊ϕ C2) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✗
[96, 202] (C2 × SL(2, 3)) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✗
[96, 203] (C2 × C2 × Q8) ⋊ϕ C3 ✔ ✗ ✗ ✗ ✔
[96, 204] ((C2 × D4) ⋊ϕ C2) ⋊ϕ C3 ✔ ✗ ✗ ✗ ✔
[96, 205] C2 × C2 × (C3 ⋊ϕ Q8) ✗ ✗ ✗ ✗ ✗
[96, 206] C2 × C2 × C4 × S3 ✗ ✗ ✗ ✗ ✗
[96, 207] C2 × C2 × D12 ✗ ✗ ✗ ✗ ✗
[96, 208] C2 × ((C12 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[96, 209] C2 × D4 × S3 ✗ ✗ ✗ ✗ ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[96, 210] C2 × ((C2 × (C3 ⋊ϕ C4)) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 211] (C6 × D4) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 212] C2 × Q8 × S3 ✗ ✗ ✗ ✗ ✗
[96, 213] C2 × ((C4 × S3) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 214] (C6 × Q8) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 215] ((C4 × C2) ⋊ϕ C2) × S3 ✗ ✗ ✗ ✗ ✗
[96, 216] (D4 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 217] (Q8 × S3) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[96, 218] C2 × C2 × C2 × (C3 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[96, 219] C2 × C2 × ((C6 × C2) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 220] C12 × C2 × C2 × C2 ✗ r r r ✗
[96, 221] C2 × C6 × D4 ✗ ✗ ✗ ✗ ✗
[96, 222] C2 × C6 × Q8 ✗ ✗ ✗ ✗ ✗
[96, 223] C6 × ((C4 × C2) ⋊ϕ C2) ✗ ✔ ✗ ✔ ✗
[96, 224] C3 × ((C2 × D4) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 225] C3 × ((C2 × Q8) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[96, 226] C2 × C2 × S4 ✔ ✗ ✗ ✗ ✔
[96, 227] ((C2 × C2 × C2 × C2) ⋊ϕ C3) ⋊ϕ C2 ✔ ✗ ✗ ✗ ✔
[96, 228] C2 × C2 × C2 × A4 ✔ ✗ ✗ ✗ ✔
[96, 229] C2 × ((C2 × C2 × C2 × C2) ⋊ϕ C3) ✔ ✗ ✗ ✗ ✔
[96, 230] C2 × C2 × C2 × C2 × S3 ✗ ✗ ✗ ✗ ✗
[96, 231] C6 × C2 × C2 × C2 × C2 ✗ r r r ✗
[97, 1] C97 ✗ r r r ✗
[98, 1] D49 ✗ ✔ ✔ ✔ ✗
[98, 2] C98 ✗ r r r ✗
[98, 3] C7 × D7 ✗ ✔ ✔ ✔ ✗
[98, 4] (C7 × C7) ⋊ϕ C2 ✗ ✗ ✗ ✗ ✗
[98, 5] C14 × C7 ✗ r r r ✗
[99, 1] C99 ✗ r r r ✗
[99, 2] C33 × C3 ✗ r r r ✗
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Tribimaximal Mixing From Small Groups K. Parattu, A. Wingerter
Table 1 – continued from previous page
GAP ID Group 3 U3 U2 U2×1 A4
[100, 1] C25 ⋊ϕ C4 ✗ ✔ ✔ ✔ ✗
[100, 2] C100 ✗ r r r ✗
[100, 3] C25 ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[100, 4] D50 ✗ ✔ ✔ ✔ ✗
[100, 5] C50 × C2 ✗ r r r ✗
[100, 6] C5 × (C5 ⋊ϕ C4) ✗ ✔ ✔ ✔ ✗
[100, 7] (C5 × C5) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[100, 8] C20 × C5 ✗ r r r ✗
[100, 9] C5 × (C5 ⋊ϕ C4) ✗ ✗ ✗ ✗ ✗
[100, 10] (C5 × C5) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[100, 11] (C5 × C5) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[100, 12] (C5 × C5) ⋊ϕ C4 ✗ ✗ ✗ ✗ ✗
[100, 13] D5 × D5 ✗ ✗ ✗ ✗ ✗
[100, 14] C10 × D5 ✗ ✔ ✔ ✔ ✗
[100, 15] C2 × ((C5 × C5) ⋊ϕ C2) ✗ ✗ ✗ ✗ ✗
[100, 16] C10 × C10 ✗ r r r ✗
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