Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for Th

Name:
Th
Group order:
90745943887872000 = 215 ⋅ 310 ⋅ 53 ⋅ 72 ⋅ 13 ⋅ 19 ⋅ 31
Number of classes:
48
InfoText value:
origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13,19,31]
Maximal subgroups:
  Order Index Structure Name
1 634023936 143127000 3D4(2).3 3D4(2).3
2 319979520 283599225 25.L5(2) 2^5.psl(5,2)
3 92897280 976841775 21+8+.A9 2^1+8.a9
4 33094656 2742012000 U3(8).6 U3(8).6
5 25474176 3562272000 (3 × G2(3)):2 (3xG2(3)):2
6 944784 96049408000 [39].2S4 ThN3B
7 944784 96049408000 32.[37].2S4 ThM7
8 349920 259333401600 35:2S6 3^5:2S6
9 12000 7562161990656 51+2:4S4 5^(1+2):4S4
10 12000 7562161990656 52:4S5 5^2:4s5
11 7056 12860819712000 72:(3 × 2S4) 7^2:(3x2S4)
12 6840 13266950860800 L2(19).2 L2(19).2
13 5616 16158465792000 L3(3) L3(3)
14 720 126036033177600 A6.23 A6.2_3
15 465 195152567500800 31:15 31:15
16 120 756216199065600 S5 A5.2
Stored Sylow p normalizers:
p Order Index Structure Name
2 32768 2769346432125 ThN2 ThN2
3 236196 384197632000 ThN3 ThN3
5 12000 7562161990656 51+2:4S4 5^(1+2):4S4
7 7056 12860819712000 72:(3 × 2S4) 7^2:(3x2S4)
13 468 193901589504000 (3 × 13:6).2 (3x13:6).2
19 342 265339017216000 19:18 19:18
31 465 195152567500800 31:15 31:15
Available Brauer tables:
p  
13 dec. matrix (PDF)
19 dec. matrix (PDF)
31 dec. matrix (PDF)
Atlas representations:
8 available
Group constructions in GAP:
AtlasGroup( "Th" ), AtlasSubgroup( "B", 5 )
Stored class fusions from this table:
B
Stored class fusions to this table:
21+8+.A9, 25.24.L4(2), 25.26.(2 × L3(2)), 25.26.D8.S3, 25.L5(2), 21+8.22.(3 × A5).2, 21+8.22.S32, 21+8.23.22.S3, 21+8.24.2.S3, 21+8.24.S32, 21+8.21+4.S3, 21+8.D8.S3, 3D4(2).3, 35:2S6, 52:4S5, 51+2:4S4, 72:(3 × 2S4), 19:18, 31:15, (25.26)a.(S3 × L3(2)), (25.26)b.(L3(2) × S3), (25.26.22)a.S32, (25.26.22)b.S32, (21+8.23)a.L3(2), (21+8.23)b.L3(2), (3 × 13:6).2, (3 × G2(3)):2, (7:3 × L2(7)):2, S5, A6.23, L2(19).2, L3(3), 32.[37].2S4, ThN2, ThN3, [39].2S4, U3(8).6

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