GAP Package AtlasRep

AtlasRep Info for He

→ ATLAS page for He

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

1	G ≤ Sym(2058)	rank 5, on cosets of S4(4):2 (1st max.)
3	G ≤ Sym(8330)	rank 7, on cosets of 22.L3(4).S3 (2nd max.)
5	G ≤ Sym(29155)	rank 12, on cosets of 26:3.S6 (3rd max.)
6	G ≤ Sym(244800)	rank 36, on cosets of 72:2L2(7) (6th max.)
7	G ≤ GL(51,2)
8	G ≤ GL(101,2)
9	G ≤ GL(246,2)
10	G ≤ GL(680,2)	character 680a
11	G ≤ GL(679,3)	character 679a
12	G ≤ GL(104,5)
13	G ≤ GL(680,5)	character 680a
14	G ≤ GL(50,7)	character 50a
15	G ≤ GL(153,7)	character 153a
16	G ≤ GL(426,7)	character 426a
17	G ≤ GL(798,7)	character 798a
18	G ≤ GL(51,9)
19	G ≤ GL(153a,9)
20	G ≤ GL(153b,9)
21	G ≤ GL(102,17)	character 51ab
22	G ≤ GL(306,17)	character 153ab
23	G ≤ GL(680,17)	character 680a
24	G ≤ GL(51,25)
25	G ≤ GL(153a,25)
26	G ≤ GL(153b,25)
27	G ≤ GL(925a,25)
28	G ≤ GL(925b,25)
29	G ≤ GL(102,ℤ)	character 51ab

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

• presentation:
• repr. cyc. subg.:
• std. gen. finder:
• automorphisms:

  2

• maxes (all 11):

  1	S4(4).2
  2	22.L3(4).S3
  3	26:3.S6
  4	26:3.S6
  5	21+6+.L3(2)
  6	72:2L2(7)
  7	3.A7.2
  8	71+2:(S3 × 3)
  9	S4 × L3(2)
  10	7:3 × L3(2)
  11	52:4A4

• std. gen. checker:

  (check)

  (pres)

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