Overview of the GAP Character Table Library (version 1.3.8)

Character Table info for G₂(4)

Name:

G2(4)

Group order:

251596800 = 2¹² ⋅ 3³ ⋅ 5² ⋅ 7 ⋅ 13

Number of classes:

32

InfoText value:

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

Maximal subgroups:

	Order	Index	Structure	Name
1	604800	416	J2	J2
2	184320	1365	22+8:(3 × A5)	2^(2+8):(3xA5)
3	184320	1365	24+6:(A5 × 3)	2^(4+6):(A5x3)
4	124800	2016	U3(4).2	U3(4).2
5	120960	2080	3.L3(4).23	3.L3(4).2_3
6	12096	20800	U3(3).2	U3(3).2
7	3600	69888	A5 × A5	A5xA5
8	1092	230400	L2(13)	L2(13)

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	36864	6825	G2(4)N2	G2(4)N2
3	432	582400	31+2:SD16	3^(1+2):SD16
5	300	838656	52:D12	5^2:D12
7	126	1996800	(7:3 × 3):2	(7:3x3):2
13	78	3225600	13:6	13:6

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:

33 available

Group constructions in GAP:

AtlasGroup( "G2(4)" ), AtlasStabilizer( "Suz", "SuzG1-p1782B0" ), AtlasSubgroup( "G2(4).2", 1 ), AtlasSubgroup( "Suz", 1 ), PrimitiveGroup( 416, 7 ), PrimitiveGroup( 1365, 1 ), PrimitiveGroup( 1365, 2 ), PrimitiveGroup( 2016, 7 ), PrimitiveGroup( 2080, 7 )

Stored class fusions from this table:

³D₄(4), G₂(4).2, Suz

Stored class fusions to this table:

2.G₂(4), 2²⁺⁸:(3 × A₅), 2⁴⁺⁶:(A₅ × 3), 3.L₃(4).2₃, 3¹⁺²:SD₁₆, 5²:D₁₂, 13:6, (7:3 × 3):2, A₅ × A₅, D₁₀ × A₅, G₂(4)N2, J₂, L₂(13), S₃ × A₅, U₃(3).2, U₃(4).2, A₅ × D₁₀

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