GAP Package AtlasRep

AtlasRep Info for HS.2

→ ATLAS page for HS.2

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

1	G ≤ Sym(100)	rank 3, on cosets of M22.2 (2nd max.)
3	G ≤ Sym(352)	rank 4, on cosets of U3(5).2 < HS
6	G ≤ Sym(1100b)	rank 5, on cosets of S8 × 2 (4th max.)
17	G ≤ Sym(15400)	rank 20, on cosets of (2 × A6.22).2 (8th max.)
19	G ≤ GL(20,2)
20	G ≤ GL(22,2)
21	G ≤ GL(56,2)
22	G ≤ GL(132,2)
23	G ≤ GL(518,2)
24	G ≤ GL(1000,2)
25	G ≤ GL(1408,2)
26	G ≤ GL(1792,2)
27	G ≤ GL(22a,3)
28	G ≤ GL(77a,3)
29	G ≤ GL(98a,3)
30	G ≤ GL(154a,3)
31	G ≤ GL(231a,3)
32	G ≤ GL(308a,3)
33	G ≤ GL(321a,3)
34	G ≤ GL(693a,3)
35	G ≤ GL(748a,3)
36	G ≤ GL(825a,3)
37	G ≤ GL(21a,5)
38	G ≤ GL(55a,5)
39	G ≤ GL(98a,5)
40	G ≤ GL(175a,5)
41	G ≤ GL(210a,5)
42	G ≤ GL(266a,5)
43	G ≤ GL(518a,5)
44	G ≤ GL(560a,5)
45	G ≤ GL(650a,5)
46	G ≤ GL(22a,7)
47	G ≤ GL(77a,7)
48	G ≤ GL(154a,7)
49	G ≤ GL(175a,7)
50	G ≤ GL(231a,7)
51	G ≤ GL(308a,7)
52	G ≤ GL(605a,7)
53	G ≤ GL(693,7)
54	G ≤ GL(693a,7)
55	G ≤ GL(770a,7)
56	G ≤ GL(803,7)
57	G ≤ GL(803a,7)
58	G ≤ GL(22a,11)
59	G ≤ GL(77a,11)
60	G ≤ GL(154a,11)
61	G ≤ GL(174a,11)
62	G ≤ GL(231a,11)
63	G ≤ GL(308a,11)
64	G ≤ GL(693a,11)
65	G ≤ GL(770a,11)
66	G ≤ GL(825a,11)
67	G ≤ GL(854a,11)
68	G ≤ GL(896a,11)

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

• presentation:
• std. gen. finder:
• maxes (all 10):

  1	HS
  1	HS
  2	M22.2
  2	M22.2
  2	M22.2
  3	L3(4).22
  4	S8 × 2
  4	S8 × 2
  5	25.S6
  6	43:(L3(2) × 2)
  6	43:(L3(2) × 2)
  7	21+6+:S5
  8	(2 × A6.22).2
  9	51+2+:[25]
  10	5:4 × S5

• std. gen. checker:

  (check)

  (pres)

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