Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for U₆(2)

Name:

U6(2)

Group order:

9196830720 = 2¹⁵ ⋅ 3⁶ ⋅ 5 ⋅ 7 ⋅ 11

Number of classes:

46

InfoText value:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	13685760	672	U5(2)	U5(2)
2	13271040	693	21+8+:U4(2)	2^(1+8)_+:U4(2)
3	10321920	891	29.L3(4)	2^9.L3(4)
4	6531840	1408	U4(3).22	U4(3).2_2
5	6531840	1408	U4(3).22	U6(2)M5
6	6531840	1408	U4(3).22	U6(2)M6
7	1474560	6237	24+8:(S3 × A5)	2^(4+8):(S3xA5)
8	1451520	6336	S6(2)	S6(2)
9	1451520	6336	S6(2)	U6(2)M9
10	1451520	6336	S6(2)	U6(2)M10
11	443520	20736	M22	M22
12	443520	20736	M22	U6(2)M12
13	443520	20736	M22	U6(2)M13
14	155520	59136	S3 × U4(2)	S3xU4(2)
15	93312	98560	31+4.21+1+2+2.S3	3^(1+4).2^(1+1+2+2).S3
16	40320	228096	L3(4).21	L3(4).2_1

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	98304	93555	24+8.(2 × A4)	2^(4+8).(2xA4)
3	5832	1576960	34:32:D8	3^4:3^2:D8
5	120	76640256	S3 × 5:4	S3x5:4
7	42	218972160	7:6	7:6
11	55	167215104	11:5	11:5

Available Brauer tables:

p
2	dec. matrix (PDF)
3	dec. matrix (PDF)
5	dec. matrix (PDF)
7	dec. matrix (PDF)
11	dec. matrix (PDF)

Atlas representations:

47 available

Group constructions in GAP:

AtlasGroup( "U6(2)" ), PSU( 6, 2 ), PrimitiveGroup( 672, 1 ), PrimitiveGroup( 693, 1 ), PrimitiveGroup( 891, 1 ), PrimitiveGroup( 1408, 3 )

Stored class fusions from this table:

U₆(2).2, U₆(2).3

Stored class fusions to this table:

2.U₆(2), 2².U₆(2), 2⁹.2⁴.A₅a, 2⁹.2⁴.A₅b, 2⁹.L₃(4), 2¹⁺⁸₊:U₄(2), 2⁴⁺⁸.(2 × A₄), 2⁴⁺⁸:(A₄ × S₃), 2⁴⁺⁸:(S₃ × A₅), 3.U₆(2), 3⁴:3²:D₈, 3⁴:S₆, 3¹⁺⁴.2^1+1+2+2.S₃, 6.U₆(2), 7:6, 11:5, (2² × 3).U₆(2), L₃(4).2₁, M₂₂, S₃ × 5:4, S₃ × U₄(2), S₆(2), U₄(3).2₂, U₅(2), U₄(3).2₂, U₄(3).2₂, S₆(2), S₆(2), M₂₂, M₂₂

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