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AtlasRep Info for Fi₂₃

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Representations for G = Fi₂₃: (all refer to std. generators 1)

1	G ≤ Sym(31671)	rank 3, on cosets of 2.Fi22 (1st max.)
2	G ≤ Sym(137632)	rank 3, on cosets of O8+(3):S3 (2nd max.)
3	G ≤ Sym(275264)	rank 5, on cosets of O8+(3).3 < O8+(3):S3
6	G ≤ GL(782,2)	character 782a
7	G ≤ GL(1494,2)	character 1494a
8	G ≤ GL(253,3)
9	G ≤ GL(528,3)
10	G ≤ GL(782,5)	character 782a
11	G ≤ GL(782,7)	character 782a
12	G ≤ GL(782,11)	character 782a
13	G ≤ GL(782,13)	character 782a
14	G ≤ GL(782,17)
15	G ≤ GL(782,23)

Programs for G = Fi₂₃: (all refer to std. generators 1)

• repr. cyc. subg.:
• std. gen. checker:
• std. gen. finder:
• maxes (10 out of 14):

  1	2.Fi22
  1	2.Fi22
  1	2.Fi22
  1	2.Fi22
  2	O8+(3).3.2
  3	22.U6(2).2
  3	22.U6(2).2
  4	S8(2)
  5	S3 × O7(3)
  6	211.M23
  9	S12
  9	S12
  10	(22 × 21+8).(3 × U4(2)).2
  13	S4(4).4
  13	S4(4).4
  14	L2(23)
  14	L2(23)

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