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AtlasRep Info for Fi₂₂

→ ATLAS page for Fi₂₂

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Representations for G = Fi₂₂: (all refer to std. generators 1)

1	G ≤ Sym(3510)	rank 3, on cosets of 2.U6(2) (1st max.)
3	G ≤ Sym(14080b)	rank 3, on cosets of O7(3) (3rd max.)
4	G ≤ Sym(61776)	rank 4, on cosets of O8+(2):S3 (4th max.)
6	G ≤ Sym(142155)	rank 8, on cosets of 210:M22 (5th max.)
8	G ≤ Sym(694980)	rank 10, on cosets of 26:S6(2) (6th max.)
10	G ≤ GL(78,2)	character 78a
11	G ≤ GL(350,2)	character 350a
12	G ≤ GL(572,2)	character 572a
13	G ≤ GL(77,3)	character 77a
14	G ≤ GL(351,3)	character 351a
15	G ≤ GL(924,3)	character 924a
16	G ≤ GL(78,5)	character 78a
17	G ≤ GL(428,5)	character 428a
18	G ≤ GL(78,7)	character 78a
19	G ≤ GL(429,7)	character 429a
20	G ≤ GL(78,11)	character 78a
21	G ≤ GL(429,11)	character 429a
22	G ≤ GL(78,13)	character 78a
23	G ≤ GL(429,13)	character 429a
24	G ≤ GL(78,ℤ)	character 78a

Programs for G = Fi₂₂: (all refer to std. generators 1)

• presentation:
• repr. cyc. subg.:
• std. gen. finder:
• maxes (all 14):

  1	2.U6(2)
  1	2.U6(2)
  2	O7(3)
  2	O7(3)
  3	O7(3)
  3	O7(3)
  3	O7(3)
  4	O8+(2).3.2
  5	210:M22
  6	26:S6(2)
  7	(2 × 21+8):U4(2):2
  8	S3 × U4(3).22
  9	2F4(2)'
  9	2F4(2)'
  10	25+8:(S3 × A6)
  11	31+6:23+4:32:2
  12	S10
  13	S10
  13	S10
  14	M12

• std. gen. checker:

  (check)

  (pres)

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