Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for J₄

Name:

J4

Group order:

86775571046077562880 = 2²¹ ⋅ 3³ ⋅ 5 ⋅ 7 ⋅ 11³ ⋅ 23 ⋅ 29 ⋅ 31 ⋅ 37 ⋅ 43

Number of classes:

62

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,23,29,31,37,43]

Maximal subgroups:

	Order	Index	Structure	Name
1	501397585920	173067389	211:M24	mx1j4
2	21799895040	3980549947	21+12+.3.M22.2	c2aj4
3	10239344640	8474719242	210:L5(2)	2^10:L5(2)
4	660602880	131358148251	23+12.(S5 × L3(2))	J4M4
5	141831360	611822174208	U3(11).2	U3(11).2
6	887040	97825995497472	M22.2	M22.2
7	319440	271649045348352	11+1+2:(5 × 2S4)	11+^(1+2):(5x2S4)
8	163680	530153782050816	L2(32).5	L2(32).5
9	12144	7145550975467520	L2(23).2	L2(23).2
10	6048	14347812672962560	U3(3)	U3(3)
11	812	106866466805514240	29:28	frob
12	602	144145466853949440	43:14	43:14
13	444	195440475329003520	37:12	37:12

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
3	864	100434688710737920	(2 × 31+2+:8):2	(2x3^(1+2)_+:8):2
5	26880	3228257851416576	(D10 × 23.L3(2)).2	(D10x2^3.L3(2)).2
7	2520	34434750415110144	7:3 × S5	7:3xS5
11	319440	271649045348352	11+1+2:(5 × 2S4)	11+^(1+2):(5x2S4)
23	506	171493223411220480	23:22	23:22
29	812	106866466805514240	29:28	frob
31	310	279921196922830848	31:10	31:10
37	444	195440475329003520	37:12	37:12
43	602	144145466853949440	43:14	43:14

Available Brauer tables:

p
5	dec. matrix (PDF)
7	dec. matrix (PDF)
37	dec. matrix (PDF)

Atlas representations:

3 available

Group constructions in GAP:

AtlasGroup( "J4" )

Stored class fusions to this table:

2¹⁰:L₅(2), 2¹¹.2⁶.3¹⁺².D₈, 6.M₂₂.2, 7:3 × S₅, 11⁺¹⁺²:(5 × 2S₄), 23:22, 31:10, 37:12, 43:14, (2 × 3¹⁺²₊:8):2, (D₁₀ × 2³.L₃(2)).2, 2³⁺¹².(S₅ × L₃(2)), L₂(23).2, L₂(32).5, M₂₂.2, M₂₄, NDG(J₄, 3²), U₃(3), U₃(11).2, 2¹⁺¹²₊.3.M₂₂.2, 29:28, 2¹¹:M₂₄

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