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AtlasRep Info for S₄(5)

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Representations for G = S₄(5): (all refer to std. generators 1)

1	G ≤ Sym(156a)	rank 3, on cosets of 51+2+:4A5 (1st max.)
2	G ≤ Sym(156b)	rank 3, on cosets of 53:(2 × A5).2 (2nd max.)
3	G ≤ Sym(300)	rank 4, on cosets of L2(25):22 (3rd max.)
4	G ≤ Sym(325)	rank 4, on cosets of 2.(A5 × A5).2 (4th max.)
5	G ≤ GL(12a,4)
6	G ≤ GL(5,5)
7	G ≤ GL(13,9)
8	G ≤ GL(40,ℤ)
9	G ≤ GL(65a,ℤ)
10	G ≤ GL(65b,ℤ)
11	G ≤ GL(90,ℤ)
12	G ≤ GL(104a,ℤ)
13	G ≤ GL(104b,ℤ)
14	G ≤ GL(104c,ℤ)
15	G ≤ GL(130,ℤ)
16	G ≤ GL(156,ℤ)
17	G ≤ GL(416,ℤ)
18	G ≤ GL(13a,Field([Sqrt(5)]))
19	G ≤ GL(13b,Field([Sqrt(5)]))

Programs for G = S₄(5): (all refer to std. generators 1)

• std. gen. checker:
• maxes (all 8):

  1	51+2+:4A5
  2	53:(2 × A5).2
  3	L2(25).22
  4	2.(A5 × A5).2
  5	24:A5
  6	S5 × S3
  7	(22 × A5):2
  8	A6

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