Character Table info for Th
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Name:
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Th
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Group order:
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90745943887872000 = 215 ⋅ 310 ⋅ 53 ⋅ 72 ⋅ 13 ⋅ 19 ⋅ 31
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Number of classes:
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48
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InfoText value:
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origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,13,19,31]
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Maximal subgroups:
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|
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 |
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Stored Sylow p normalizers:
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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 |
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Available Brauer tables:
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Atlas representations:
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8 available
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Group constructions in GAP:
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AtlasGroup( "Th" )
,
AtlasSubgroup( "B", 5 )
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Stored class fusions from this table:
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B
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Stored class fusions to this table:
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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