Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for B

Name:

B

Group order:

4154781481226426191177580544000000 = 2⁴¹ ⋅ 3¹³ ⋅ 5⁶ ⋅ 7² ⋅ 11 ⋅ 13 ⋅ 17 ⋅ 19 ⋅ 23 ⋅ 31 ⋅ 47

Number of classes:

184

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r.

Maximal subgroups:

	Order	Index	Structure	Name
1	306129918735099415756800	13571955000	2.2E6(2).2	2.2E6(2).2
2	354883595661213696000	11707448673375	21+22.Co2	2^(1+22).Co2
3	4089470473293004800	1015970529280000	Fi23	Fi23
4	1589728887019929600	2613515747968125	29+16.S8(2)	2^(9+16).S8(2)
5	90745943887872000	45784762417152000	Th	Th
6	26489012826931200	156849238149120000	(22 × F4(2)):2	(2^2xF4(2)):2
7	22858846741463040	181758140654146875	22+10+20.(M22.2 × S3)	2^(2+10+20).(M22.2xS3)
8	10736731045232640	386968944618506250	[230].L5(2)	[2^30].L5(2)
9	774741019852800	5362800438804480000	S3 × Fi22.2	S3xFi22.2
10	692692325498880	5998018641586846875	[235].(S5 × L3(2))	[2^35].(S5xL3(2))
11	546061824000000	7608628361513926656	HN.2	HN.2
12	118852315545600	34957513971466240000	O8+(3).S4	O8+(3).S4
13	130606940160	31811337714034278400000	31+8.21+6.U4(2).2	3^(1+8).2^(1+6).U4(2).2
14	1881169920	2208615732717237043200000	(32:D8 × U4(3).22).2	(3^2:D8xU4(3).2^2).2
15	1774080000	2341935809673986624716800	5:4 × HS.2	5:4xHS.2
16	862617600	4816481232502590013440000	S4 × 2F4(2)'.2	S4x2F4(2)'.2
17	204073344	20359256136981938176000000	32.33.36.(S4 × 2S4)	3^2.3^3.3^6.(S4x2S4)
18	106444800	39032263494566443745280000	A5.2 × M22.2	A5.2xM22.2
19	58060800	71559149740038480199680000	(S6 × L3(4).2).2	(S6xL3(4).2).2
20	46500000	89350139381213466476937216	53.L3(5)	5^3.psl(3,5)
21	24000000	173115895051101091299065856	51+4.21+4.A5.4	5^(1+4).2^(1+4).A5.4
22	2073600	2003656192721077445591040000	(S6 × S6).4	(S6xS6).4
23	288000	14426324587591757608255488000	52:4S4 × S5	5^2:4S4xS5
24	117600	35329774500224712510013440000	L2(49).23	L2(49).2_3
25	14880	279219185566292082740428800000	L2(31)	L2(31)
26	7920	524593621366973003936563200000	M11	M11
27	5616	739811517312397826064384000000	L3(3)	L3(3)
28	4896	848607328681868094603264000000	L2(17).2	L2(17).2
29	1320	3147561728201838023619379200000	L2(11).2	L2(11).2
30	1081	3843461129719173164826624000000	47:23	47:23

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
3	12754584	325748098191711010816000000	Fi23N3	Fi23N3
5	250000	16619125924905704764710322176	LyN5	LyN5
7	28224	147207393750936302125056000000	BN7	BN7
31	465	8935013938121346647693721600000	31:15	31:15

Available Brauer tables:

p
11	dec. matrix (PDF)
13	dec. matrix (PDF)
17	dec. matrix (PDF)
23	dec. matrix (PDF)
31	dec. matrix (PDF)

Atlas representations:

3 available

Group constructions in GAP:

AtlasGroup( "B" )

Stored class fusions to this table:

2.²E₆(2).2, 2.B, 2¹⁺²².Co₂, 2^2+10+20.(M₂₂.2 × S₃), 2⁹⁺¹⁶.S₈(2), 2 × 23:11, 3².3³.3⁶.(S₄ × 2S₄), 3¹⁺⁸.2¹⁺⁶.U₄(2).2, 3³⁺⁶:(L₃(3) × D₈), 5:4 × HS.2, 5²:4S₄ × S₅, 5³.L₃(5), 5¹⁺⁴.2¹⁺⁴.A₅.4, 31:15, 47:23, (3²:D₈ × U₄(3).2²).2, (S₆ × L₃(4).2).2, (S₆ × S₆).4, A₅.2 × M₂₂.2, BN7, D₈ × ²F₄(2)'.2, Fi₂₃, Fi₂₃N3, HN.2, L₂(11).2, L₂(17).2, L₂(31), L₂(49).2₃, L₃(3), LyN5, M₁₁, O₈⁺(3), O₈⁺(3).S₄, S₃ × Fi₂₂.2, S₄ × ²F₄(2)'.2, Th, [2³⁰].L₅(2), [2³⁵].(S₅ × L₃(2))

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