Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for G₂(4).2

Name:

G2(4).2

Group order:

503193600 = 2¹³ ⋅ 3³ ⋅ 5² ⋅ 7 ⋅ 13

Number of classes:

40

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., constructions: Aut(G2(4))

Maximal subgroups:

	Order	Index	Structure	Name
1	251596800	2	G2(4)	G2(4)
2	1209600	416	J2.2	J2.2
3	368640	1365	22+8:(3 × A5):2	2^(2+8):(3xA5):2
4	368640	1365	24+6:(A5 × 3):2	2^(4+6):(A5x3):2
5	249600	2016	U3(4).4	U3(4).4
6	241920	2080	3.L3(4).22	3.L3(4).2^2
7	24192	20800	2 × U3(3).2	2xU3(3).2
8	7200	69888	(A5 × A5):2	(A5xA5):2
9	2184	230400	L2(13).2	L2(13).2

Available Brauer tables:

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

Atlas representations:

11 available

Group constructions in GAP:

AtlasGroup( "G2(4).2" ), AtlasStabilizer( "Suz.2", "Suzd2G1-p1782B0" ), AtlasSubgroup( "Suz.2", 2 ), AutomorphismGroup( AtlasGroup( "G2(4)" ) ), PrimitiveGroup( 416, 4 ), PrimitiveGroup( 1365, 3 ), PrimitiveGroup( 1365, 4 ), PrimitiveGroup( 2016, 8 ), PrimitiveGroup( 2080, 8 )

Stored class fusions from this table:

Suz.2

Stored class fusions to this table:

2.G₂(4).2, 2²⁺⁸:(3 × A₅):2, 2⁴⁺⁶:(A₅ × 3):2, 2 × U₃(3).2, 3.L₃(4).2², 5²:(4 × S₃), 13:12, (3 × G₂(4)).2, (A₄ × G₂(4)):2, (A₅ × A₅):2, (A₅ × D₁₀).2, (D₁₀ × A₅).2, G₂(4), Isoclinic(2.G₂(4).2), J₂.2, L₂(13).2, S₃ × 7:6, S₅ × S₃, U₃(4).4

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