Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for 2.Fi22

Name:
2.Fi22
Group order:
129123503308800 = 218 ⋅ 39 ⋅ 52 ⋅ 7 ⋅ 11 ⋅ 13
Number of classes:
114
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r.
Duplicates:
2.Fi22
Maximal subgroups:
  Order Index Structure Name
1 36787322880 3510 22.U6(2) 2^2.U6(2)
2 9170703360 14080 2 × O7(3) 2xO7(3)
3 9170703360 14080 2 × O7(3) 2.Fi22M3
4 2090188800 61776 O8+(2):S3 × 2 O8+(2):S3x2
5 908328960 142155 211.M22 2.Fi22M5
6 185794560 694980 27:S6(2) S8(2)M3
7 106168320 1216215 2.(2 × 21+8):U4(2):2 2.(2x2^(1+8)):U4(2):2
8 78382080 1647360 S3 × 2.U4(3).22 S3x2.U4(3).2_2
9 35942400 3592512 2 × 2F4(2)' 2x2F4(2)'
10 35389440 3648645 21+5+8.(S3 × A6) 2^(1+5+8).(S3xA6)
11 10077696 12812800 2.(31+6:23+4:32:2) 2.(3^(1+6):2^(3+4):3^2:2)
12 7257600 17791488 S10 × 2 S10x2
13 7257600 17791488 S10 × 2 2.Fi22M13
14 190080 679311360 2 × M12 2xm12
Stored Sylow p normalizers:
p Order Index Structure Name
2 262144 492567075 2.Fi22N2 2.Fi22N2
3 157464 820019200 2 × Fi22N3 2xFi22N3
5 4800 26900729856 2 × Fi22N5 2xFi22N5
7 504 256197427200 2 × S3 × 7:6 2xS3x7:6
11 220 586925015040 22 × 11:5 2^2x11:5
13 156 827714764800 2 × 13:6 2x13:6
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:
12 available
Group constructions in GAP:
AtlasGroup( "2.Fi22" ), AtlasStabilizer( "Fi23", "F23G1-p31671B0" ), AtlasSubgroup( "Fi23", 1 )
Stored class fusions from this table:
2.2E6(2), 2.Fi22.2, Fi22, Fi22, Fi23
Stored class fusions to this table:
2.(2 × 21+8):U4(2):2, 2.(31+6:23+4:32:2), 2 × O7(3), 211.M22, S10 × 2, 2.Fi22N2, 2 × 2.Fi22, 22.U6(2), 22 × 11:5, 21+5+8.(S3 × A6), 2 × 2F4(2)', 2 × 35.33.(2 × S4), 2 × 35.31+2.2.S4, 2 × 35:U4(2):2, 2 × 33+3:L3(3), 2 × 3(3+3)b:L3(3), 2 × 13:6, 2 × (31+6.3)a.2.S4, 2 × (31+6.3)b.2.S4, 2 × Fi22N3, 2 × Fi22N5, 2 × O7(3), 2 × S3 × 7:6, 2 × M12, 5:4 × S5 × 2, 6.Fi22, 2 × 6.Fi22, O8+(2):S3 × 2, S3 × 2.U4(3).22, 27:S6(2), S10 × 2

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