Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for G₂(3)

Name:

G2(3)

Group order:

4245696 = 2⁶ ⋅ 3⁶ ⋅ 7 ⋅ 13

Number of classes:

23

InfoText value:

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

Duplicates:

O7(3)M5

Maximal subgroups:

	Order	Index	Structure	Name
1	12096	351	U3(3).2	U3(3).2
2	12096	351	U3(3).2	G2(3)M2
3	11664	364	(3(1+2)+ × 32):2S4	(3^(1+2)+x3^2):2S4
4	11664	364	(3(1+2)+ × 32):2S4	G2(3)M4
5	11232	378	L3(3).2	L3(3).2
6	11232	378	L3(3).2	G2(3)M6
7	1512	2808	L2(8).3	L2(8).3
8	1344	3159	23.L3(2)	2^3.L3(2)
9	1092	3888	L2(13)	L2(13)
10	576	7371	2(1+4)+:32.2	2^(1+4)+:3^2.2

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	64	66339	M12N2	M12N2
3	2916	1456	32.(3 × 3(1+2)+):22	3^2.(3x3^(1+2)+):2^2
7	42	101088	7:6	7:6
13	78	54432	13:6	13:6

Available Brauer tables:

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

Atlas representations:

25 available

Group constructions in GAP:

AtlasGroup( "G2(3)" ), AtlasStabilizer( "O7(3)", "O73G1-p1080aB0" ), AtlasStabilizer( "O7(3)", "O73G1-p1080bB0" ), AtlasSubgroup( "O7(3)", 4 ), PrimitiveGroup( 351, 7 ), PrimitiveGroup( 364, 5 ), PrimitiveGroup( 378, 7 ), PrimitiveGroup( 2808, 1 ), PrimitiveGroup( 3159, 1 ), PrimitiveGroup( 3888, 1 ), SimpleGroup( "G", 2, 3 )

Stored class fusions from this table:

³D₄(3), G₂(3).2, O₇(3)

Stored class fusions to this table:

2³.L₃(2), 2⁽¹⁺⁴⁾⁺:3².2, 2 × 3.G₂(3), 3.G₂(3), 3².(3 × 3⁽¹⁺²⁾⁺):2², 4²:D₁₂, 7:6, 13:6, (3⁽¹⁺²⁾⁺ × 3²):2S₄, U₃(3).2, (3⁽¹⁺²⁾⁺ × 3²):2S₄, L₃(3).2, L₂(8).3, L₂(13), L₃(3).2, M₁₂N2, U₃(3).2

File created automatically by GAP on 20-May-2025.