Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for 2.Co₁

Name:

2.Co1

Group order:

8315553613086720000 = 2²² ⋅ 3⁹ ⋅ 5⁴ ⋅ 7² ⋅ 11 ⋅ 13 ⋅ 23

Number of classes:

167

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11,13,23]

Maximal subgroups:

	Order	Index	Structure	Name
1	84610842624000	98280	2 × Co2	2xCo2
2	5380145971200	1545600	6.Suz.2	6.Suz.2
3	1002795171840	8292375	2.211:M24	2.2^11:M24
4	991533312000	8386560	2 × Co3	2xCo3
5	178362777600	46621575	(2 × 21+8+).O8+(2)	(2x2^(1+8)_+).O8+(2)
6	110361968640	75348000	2 × U6(2).3.2	2xU6(2).3.2
7	12076646400	688564800	2.(A4 × G2(4)).2	2.(A4xG2(4)).2
8	3963617280	2097970875	2.22+12:(A8 × S3)	2.2^(2+12):(A8xS3)
9	1698693120	4895265375	2.24+12.(S3 × 3S6)	2.2^(4+12).(S3x3S6)
10	470292480	17681664000	(32 × 2).U4(3).D8	(3^2x2).U4(3).D8
11	277136640	30005248000	2 × 36:2.M12	2x3^6:2.M12
12	145152000	57288591360	2.(A5 × J2).2	2.(A5xJ2).2
13	50388480	165028864000	2 × 31+4.2U4(2).2	2x3^(1+4).2U4(2).2
14	8709120	954809856000	(2.A6 × U3(3)).2	(2.A6xU3(3)).2
15	5038848	1650288640000	33+4:(2.S4)2	3^(3+4):(2.S4)^2
16	2177280	3819239424000	2.A9 × S3	2.A9xS3
17	1693440	4910450688000	(2.A7 × L2(7)).2	(2.A7xL2(7)).2
18	288000	28873450045440	(D10 × 2.(A5 × A5).2).2	(D10x2.(A5xA5).2).2
19	120000	69296280109056	2 × 51+2:GL2(5)	2x5^(1+2):GL2(5)
20	120000	69296280109056	53:(4 × (2 × A5).2)	5^3:(4x(2xA5).2)
21	7056	1178508165120000	2 × 72:(3 × 2A4)	2x7^2:(3x2A4)
22	6000	1385925602181120	2 × 52:2A5	2x5^2:2A5

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
3	314928	26404618240000	2 × Co1N3	2xCo1N3
5	20000	415777680654336	2 × Co1N5	2xCo1N5
7	7056	1178508165120000	2 × 72:(3 × 2A4)	2x7^2:(3x2A4)
11	1320	6299661828096000	(11:5 × D12).2	(11:5xD12).2
13	3744	2221034618880000	2.(13:6 × A4).2	2.(13:6xA4).2

Available Brauer tables:

p
7	dec. matrix (PDF)
11	dec. matrix (PDF)
13	dec. matrix (PDF)
23	dec. matrix (PDF)

Atlas representations:

9 available

Group constructions in GAP:

AtlasGroup( "2.Co1" )

Stored class fusions from this table:

Co₁

Stored class fusions to this table:

2.2¹¹:M₂₄, 2.2²⁺¹²:(A₈ × S₃), 2.2⁴⁺¹².(S₃ × 3S₆), 2.(13:6 × A₄).2, 2.(A₄ × G₂(4)).2, 2.(A₅ × J₂).2, 2.(D₁₀ × J₂).2, 2.A₉ × S₃, 2¹⁺²⁴.2.Co₁, 2 × 3⁶:2.M₁₂, 2 × 3¹⁺⁴.2U₄(2).2, 2 × 5²:2A₅, 2 × 5¹⁺²:GL₂(5), 2 × 7²:(3 × 2A₄), 2 × 23:11, 2 × (7:3 × L₂(7)):2, 2 × Co₁N3, 2 × Co₁N5, 2 × Co₂, 2 × Co₃, 2 × U₆(2).3.2, 3³⁺⁴:(2.S₄)², 5³:(4 × (2 × A₅).2), 6.Suz.2, (2.A₆ × U₃(3)).2, (2.A₇ × L₂(7)).2, (2 × 2¹⁺⁸₊).O₈⁺(2), (3² × 2).U₄(3).D₈, (7:3 × 2.A₇):2, (11:5 × D₁₂).2, (D₁₀ × 2.(A₅ × A₅).2).2, (Q₁₆ × U₃(3)).2, NDG(2.Co₁, 3³), NDG(2.Co₁, 5²)

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