Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for 3.G₂(3)

Name:

3.G2(3)

Group order:

12737088 = 2⁶ ⋅ 3⁷ ⋅ 7 ⋅ 13

Number of classes:

45

InfoText value:

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

Duplicates:

3.O7(3)M5

Maximal subgroups:

	Order	Index	Structure	Name
1	36288	351	3 × U3(3).2	3xU3(3).2
2	36288	351	3 × U3(3).2	3.G2(3)M2
3	34992	364	3.(3(1+2)+ × 32):2S4	3.(3^(1+2)+x3^2):2S4
4	34992	364	3.(3(1+2)+ × 32):2S4	3.G2(3)M4
5	33696	378	3 × L3(3).2	3xL3(3).2
6	33696	378	3 × L3(3).2	3.G2(3)M6
7	4536	2808	3 × L2(8).3	3xL2(8).3
8	4032	3159	3 × 23.L3(2)	3x2^3.L3(2)
9	3276	3888	3 × L2(13)	3xL2(13)
10	1728	7371	3.2(1+4)+:32.2	3.2^(1+4)+:3^2.2

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	192	66339	3 × M12N2	3xM12N2
3	8748	1456	33.(3 × 3(1+2)+):22	3^3.(3x3^(1+2)+):2^2
7	126	101088	3 × 7:6	3x7:6
13	234	54432	3 × 13:6	3x13:6

Available Brauer tables:

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

Atlas representations:

4 available

Group constructions in GAP:

AtlasGroup( "3.G2(3)" ), AtlasSubgroup( "3.O7(3)", 4 )

Stored class fusions from this table:

3.G₂(3).2, 3.O₇(3), G₂(3)

Stored class fusions to this table:

3.2⁽¹⁺⁴⁾⁺:3².2, 3.(3⁽¹⁺²⁾⁺ × 3²):2S₄, 3 × U₃(3).2, 3.(3⁽¹⁺²⁾⁺ × 3²):2S₄, 3 × L₃(3).2, 3³.(3 × 3⁽¹⁺²⁾⁺):2², 3 × 2³.L₃(2), 3 × 4²:D₁₂, 3 × 7:6, 3 × 13:6, 3 × L₂(8).3, 3 × L₂(13), 3 × L₃(3).2, 3 × M₁₂N2, 3 × U₃(3).2

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