GAP Package AtlasRep

AtlasRep Info for S₆(2)

→ ATLAS page for S₆(2)

→ Overview of Groups

Representations for G = S₆(2): (all refer to std. generators 1)

1	G ≤ Sym(28)	2-trans., on cosets of U4(2).2 (1st max.)
2	G ≤ Sym(36)	2-trans., on cosets of S8 (2nd max.)
3	G ≤ Sym(56)	rank 4, on cosets of U4(2) < U4(2).2
4	G ≤ Sym(63)	rank 3, on cosets of 25:S6 (3rd max.)
5	G ≤ Sym(72)	rank 4, on cosets of A8 < S8
6	G ≤ Sym(120)	rank 3, on cosets of U3(3):2 (4th max.)
7	G ≤ Sym(126)	rank 5, on cosets of 25:A6 < 25:S6
8	G ≤ Sym(135)	rank 4, on cosets of 26:L3(2) (5th max.)
9	G ≤ Sym(240)	rank 5, on cosets of U3(3) < U3(3):2
10	G ≤ Sym(288)	rank 5, on cosets of S7 < S8
11	G ≤ Sym(315)	rank 5, on cosets of 2.[26]:(S3 × S3) (6th max.)
12	G ≤ Sym(336)	rank 5, on cosets of S3 × S6 (7th max.)
13	G ≤ Sym(378a)	rank 8, on cosets of 2 × 24:S5 < 25:S6
14	G ≤ Sym(378b)	rank 6, on cosets of 25:S5 < 25:S6
15	G ≤ Sym(960)	rank 6, on cosets of L2(8).3 (8th max.)
16	G ≤ GL(6,2)	character 6a
17	G ≤ GL(8,2)	character 8a
18	G ≤ GL(14,2)	character 14a
19	G ≤ GL(48,2)	character 48a
20	G ≤ GL(64,2)	character 64a
21	G ≤ GL(112,2)	character 112a
22	G ≤ GL(512,2)	character 512a
23	G ≤ GL(7,3)	character 7a
24	G ≤ GL(14,3)	character 14a
25	G ≤ GL(21,3)	character 21a
26	G ≤ GL(27,3)	character 27a
27	G ≤ GL(34,3)	character 34a
28	G ≤ GL(35,3)	character 35a
29	G ≤ GL(49,3)	character 49a
30	G ≤ GL(91,3)	character 91a
31	G ≤ GL(98,3)	character 98a
32	G ≤ GL(189a,3)	character 189a
33	G ≤ GL(189b,3)	character 189b
34	G ≤ GL(189c,3)	character 189c
35	G ≤ GL(196,3)	character 196a
36	G ≤ GL(405,3)	character 405a
37	G ≤ GL(7,ℤ)	character 7a
38	G ≤ GL(15,ℤ)	character 15a
39	G ≤ GL(21a,ℤ)	character 21a
40	G ≤ GL(21b,ℤ)	character 21b
41	G ≤ GL(27,ℤ)	character 27a
42	G ≤ GL(35a,ℤ)	character 35a
43	G ≤ GL(35b,ℤ)	character 35b
44	G ≤ GL(56,ℤ)	character 56a
45	G ≤ GL(70,ℤ)	character 70a
46	G ≤ GL(84,ℤ)	character 84a
47	G ≤ GL(105a,ℤ)	character 105a
48	G ≤ GL(105b,ℤ)	character 105b
49	G ≤ GL(105c,ℤ)	character 105c
50	G ≤ GL(120,ℤ)	character 120a
51	G ≤ GL(168,ℤ)	character 168a
52	G ≤ GL(189a,ℤ)	character 189a
53	G ≤ GL(189b,ℤ)	character 189b
54	G ≤ GL(189c,ℤ)	character 189c
55	G ≤ GL(210a,ℤ)	character 210a
56	G ≤ GL(210b,ℤ)	character 210b
57	G ≤ GL(216,ℤ)	character 216a

Programs for G = S₆(2): (all refer to std. generators 1)

• presentation:
• repr. cyc. subg.:
• class repres.:

  (direct)

  (composed)

• maxes (all 8):

  1	U4(2).2
  2	S8
  3	25:S6
  4	U3(3).2
  5	26:L3(2)
  6	2.[26]:(S3 × S3)
  7	S3 × S6
  8	L2(8).3

• std. gen. checker:

  (check)

  (pres)

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