Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for (2² × 3).U₆(2)

Name:

(2^2x3).U6(2)

Group order:

110361968640 = 2¹⁷ ⋅ 3⁷ ⋅ 5 ⋅ 7 ⋅ 11

Number of classes:

393

InfoText value:

origin: computed in March 2000 from the tables of the factor groups 2^2.U6(2) and 6.U6(2), the subgroup 3x2^2xU5(2), and the supergroup 6.Fi22

Some maximal subgroups:

	Order	Index	Structure	Name
1	164229120	672	22 × 3 × U5(2)	2^2x3xU5(2)
2	159252480	693	3 × 22.21+8+:U4(2)	3x2^2.2^(1+8)_+:U4(2)
3	123863040	891	210:6.L3(4)	(2^2x3).U6(2)M3
4	78382080	1408	2 × 61.U4(3).22	2x6_1.U4(3).2_2
5	78382080	1408	2 × 61.U4(3).22	(2^2x3).U6(2)M5
6	78382080	1408	2 × 61.U4(3).22	(2^2x3).U6(2)M6
7	17694720	6237	3 × 22.24+8:(S3 × A5)	3x2^2.2^(4+8):(S3xA5)
8	17418240	6336	22 × 3 × S6(2)	2^2x3xS6(2)
9	17418240	6336	22 × 3 × S6(2)	(2^2x3).U6(2)M9
10	17418240	6336	22 × 3 × S6(2)	(2^2x3).U6(2)M10
11	5322240	20736	2 × 6.M22	2x6.M22
12	5322240	20736	2 × 6.M22	(2^2x3).U6(2)M12
13	5322240	20736	2 × 6.M22	(2^2x3).U6(2)M13
14	1866240	59136	22 × 3 × S3 × U4(2)	2^2x3xS3xU4(2)
15	1119744	98560	(22 × 3).(31+4.[27.3])	(2^2x3).(3^(1+4).[2^7.3])

Atlas representations:

3 available

Group constructions in GAP:

AtlasGroup( "(2^2x3).U6(2)" ), AtlasSubgroup( "6.Fi22", 1 )

Stored class fusions from this table:

2.U₆(2), 2².U₆(2), 3.U₆(2), 6.Fi₂₂, 6.U₆(2), (2² × 3).U₆(2).2, (2² × 3).U₆(2).3, U₆(2)

Stored class fusions to this table:

2² × 3 × S₃ × U₄(2), 2² × 3 × S₆(2), 2² × 3 × U₅(2), 2 × 6.M₂₂, 2 × 6₁.U₄(3).2₂, 3 × 2².2¹⁺⁸₊:U₄(2), 3 × 2².2⁴⁺⁸:(S₃ × A₅), 2¹⁰:6.L₃(4), 2 × 6₁.U₄(3).2₂, 2 × 6₁.U₄(3).2₂, 2² × 3 × S₆(2), 2² × 3 × S₆(2), 2 × 6.M₂₂, 2 × 6.M₂₂

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