Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for 3.Fi22

Name:
3.Fi22
Group order:
193685254963200 = 217 ⋅ 310 ⋅ 52 ⋅ 7 ⋅ 11 ⋅ 13
Number of classes:
165
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r.
Duplicates:
3.Fi22, 3.Fi22
Maximal subgroups:
  Order Index Structure Name
1 55180984320 3510 6.U6(2) 6.U6(2)
2 13756055040 14080 3.O7(3) 3.O7(3)
3 13756055040 14080 3.O7(3) 3.Fi22M3
4 3135283200 61776 3 × O8+(2):S3 3xO8+(2):S3
5 1362493440 142155 210:3.M22 3.Fi22M5
6 278691840 694980 3 × 26:S6(2) 3x2^6:S6(2)
7 159252480 1216215 3 × (2 × 21+8):U4(2):2 3x(2x2^(1+8)):U4(2):2
8 117573120 1647360 S3 × 31.U4(3).22 S3x3_1.U4(3).2_2
9 53913600 3592512 3 × 2F4(2)' 3x2F4(2)'
10 53084160 3648645 25+8:(S3 × 3.A6) 2^(5+8):(S3x3.A6)
11 15116544 12812800 3.31+6:23+4:32:2 3.3^(1+6):2^(3+4):3^2:2
12 10886400 17791488 3 × A10.2 3xA10.2
13 10886400 17791488 3 × A10.2 3xA10.2
14 285120 679311360 3 × M12 3xM12
Stored Sylow p normalizers:
p Order Index Structure Name
2 393216 492567075 3 × Fi22N2 3xFi22N2
3 236196 820019200 3.Fi22N3 3.Fi22N3
5 7200 26900729856 3 × Fi22N5 3xFi22N5
7 756 256197427200 3 × S3 × 7:6 3xS3x7:6
11 330 586925015040 6 × 11:5 6x11:5
13 234 827714764800 3 × 13:6 3x13:6
Available Brauer tables:
p  
2 dec. matrix (PDF)
3 dec. matrix (PDF)
5 dec. matrix (PDF)
7 dec. matrix (PDF)
11 dec. matrix (PDF)
13 dec. matrix (PDF)
Atlas representations:
8 available
Group constructions in GAP:
AtlasGroup( "3.Fi22" ), AtlasSubgroup( "3.Fi22.2", 1 )
Stored class fusions from this table:
3.2E6(2), 3.Fi22.2, Fi22
Stored class fusions to this table:
25+8:(2 × 3.A6), 25+8:(S3 × 3.A6), 2 × 6.Fi22, 3.31+6:23+4:32:2, 3.O7(3), 210:3.M22, 3.Fi22N3, 3.O7(3), 3 × 2F4(2)', 3 × 26.25.S6, 3 × 26:S6(2), 3 × 210.22.22.S4, 3 × 210.23.L3(2), 3 × 210.23.S4, 3 × 210.24.S5, 3 × 25+8:(2 × S4), 3 × 25+8:(S3 × D8), 3 × 25+8:(S3 × S4), 3 × 5:4 × S5, 3 × 13:6, 3 × (2 × 21+8):U4(2):2, 3 × (2 × 21+8+).2.24.(S3 × S3), 3 × A10.2, 3 × Fi22N2, 3 × Fi22N5, 3 × M12, 3 × O8+(2):S3, 3 × S3 × 7:6, 6.Fi22, 6.U6(2), 6 × 11:5, S3 × 31.U4(3).22

File created automatically by GAP on 13-Mar-2024.