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AtlasRep Info for U₃(7)

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Representations for G = U₃(7): (all refer to std. generators 1)

1	G ≤ Sym(344)	2-trans., on cosets of 71+2:48 (1st max.)
2	G ≤ Sym(688)	rank 4, on cosets of 71+2:24 < 71+2:48
3	G ≤ Sym(1032)	rank 6, on cosets of 71+2:16 < 71+2:48
4	G ≤ Sym(1376)	rank 8, on cosets of 71+2:12 < 71+2:48
5	G ≤ Sym(2064)	rank 12, on cosets of 71+2:8 < 71+2:48
6	G ≤ Sym(2107)	rank 8, on cosets of 2(L2(7) × 4).2 (2nd max.)
7	G ≤ Sym(14749)	rank 60, on cosets of 82:S3 (3rd max.)
8	G ≤ Sym(16856)	rank 114, on cosets of L2(7):2 (4th max.)
9	G ≤ Sym(43904)	rank 362, on cosets of 43:3 (5th max.)
10	G ≤ GL(42,2)
11	G ≤ GL(258,2)
12	G ≤ GL(344,2)
13	G ≤ GL(42,3)
14	G ≤ GL(43a,3)
15	G ≤ GL(6c,7)
16	G ≤ GL(8,7)
17	G ≤ GL(12,7)
18	G ≤ GL(20,7)
19	G ≤ GL(27,7)
20	G ≤ GL(30a,7)
21	G ≤ GL(30b,7)
22	G ≤ GL(37,7)
23	G ≤ GL(42c,7)
24	G ≤ GL(48,7)
25	G ≤ GL(42,43)
26	G ≤ GL(43a,43)
27	G ≤ GL(43a,ℤ)

Programs for G = U₃(7): (all refer to std. generators 1)

• presentation:
• std. gen. checker:
• automorphisms:

  2

• maxes (all 5):

  1	71+2:48
  2	2(L2(7) × 4).2
  3	82:S3
  4	L3(2).2
  5	43:3

File created automatically by GAP on 22-Apr-2022.