Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for Co₁

Name:

Co1

Group order:

4157776806543360000 = 2²¹ ⋅ 3⁹ ⋅ 5⁴ ⋅ 7² ⋅ 11 ⋅ 13 ⋅ 23

Number of classes:

101

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	42305421312000	98280	Co2	Co2
2	2690072985600	1545600	3.Suz.2	3.Suz.2
3	501397585920	8292375	211:M24	2^11:M24
4	495766656000	8386560	Co3	Co3
5	89181388800	46621575	2(1+8)+.O8+(2)	2^(1+8)+.O8+(2)
6	55180984320	75348000	U6(2).3.2	U6(2).3.2
7	6038323200	688564800	(A4 × G2(4)):2	(A4xG2(4)):2
8	1981808640	2097970875	22+12:(A8 × S3)	2^(2+12):(A8xS3)
9	849346560	4895265375	24+12.(S3 × 3S6)	2^(4+12).(S3x3S6)
10	235146240	17681664000	32.U4(3).D8	3^2.U4(3).D8
11	138568320	30005248000	36:2M12	3^6:2M12
12	72576000	57288591360	(A5 × J2):2	(A5xJ2):2
13	25194240	165028864000	31+4.2U4(2).2	3^(1+4).2U4(2).2
14	4354560	954809856000	(A6 × U3(3)):2	(A6xU3(3)):2
15	2519424	1650288640000	33+4:2(S4 × S4)	3^(3+4):2(S4xS4)
16	1088640	3819239424000	A9 × S3	A9xS3
17	846720	4910450688000	(A7 × L2(7)):2	(A7xL2(7)):2
18	144000	28873450045440	(D10 × (A5 × A5).2).2	(D10x(A5xA5).2).2
19	60000	69296280109056	51+2:GL2(5)	5^(1+2):GL2(5)
20	60000	69296280109056	53:(4 × S5)	5^3:(4xS5)
21	3528	1178508165120000	72:(3 × 2A4)	7^2:(3x2A4)
22	3000	1385925602181120	52:2A5	5^2:2A5

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
3	157464	26404618240000	Co1N3	Co1N3
5	10000	415777680654336	Co1N5	Co1N5
7	3528	1178508165120000	72:(3 × 2A4)	7^2:(3x2A4)
11	660	6299661828096000	11:10 × S3	11:10xS3
13	1872	2221034618880000	(13:6 × A4).2	(13:6xA4).2
23	253	16433900421120000	23:11	23:11

Available Brauer tables:

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

Atlas representations:

20 available

Group constructions in GAP:

AtlasGroup( "Co1" )

Stored class fusions to this table:

2.Co₁, 2¹⁺²⁴.2.Co₁, 2¹⁺²⁴.Co₁, 2¹¹:M₂₄, 2²⁴.Co₁, 2⁽¹⁺⁸⁾⁺.O₈⁺(2), 2²⁺¹²:(A₈ × S₃), 2⁴⁺¹².(S₃ × 3S₆), 2⁴⁺¹².(S₃ × 3¹⁺²₊:D₈), 3.Suz.2, 3².U₄(3).D₈, 3⁶:2M₁₂, 3¹⁺⁴₊.2U₄(2), 3¹⁺⁴.2U₄(2).2, 3³⁺⁴:2(S₄ × S₄), 5²:2A₅, 5³:(4 × S₅), 5¹⁺²:GL₂(5), 7²:(3 × 2A₄), 11:10 × S₃, 23:11, (7:3 × A₇):2, (13:6 × A₄).2, (A₄ × G₂(4)):2, (A₅ × J₂):2, (A₆ × U₃(3)):2, (A₇ × L₂(7)):2, (D₁₀ × (A₅ × A₅).2).2, (D₁₀ × J₂).2, A₉ × S₃, Co₁N3, Co₁N5, Co₂, Co₃, D₈ × U₃(3).2, NDG(Co₁, 5²), S₄ × U₃(3).2, U₆(2).3.2

File created automatically by GAP on 6-May-2025.