Overview of the GAP Character Table Library (version 1.3.10)

Character Table info for M₂₂

Name:

M22

Group order:

443520 = 2⁷ ⋅ 3² ⋅ 5 ⋅ 7 ⋅ 11

Number of classes:

12

InfoText value:

origin: ATLAS of finite groups, tests: 1.o.r., pow[2,3,5,7,11]

Duplicates:

McLM3, U6(2)M12, U6(2)M13

Maximal subgroups:

	Order	Index	Structure	Name
1	20160	22	L3(4)	L3(4)
2	5760	77	24:A6	2^4:a6
3	2520	176	A7	A7
4	2520	176	A7	A7
5	1920	231	24:S5	2^4:s5
6	1344	330	23:L3(2)	2^3:sl(3,2)
7	720	616	A6.23	A6.2_3
8	660	672	L2(11)	L2(11)

Stored Sylow p normalizers:

p	Order	Index	Structure	Name
2	128	3465	24:D8	2^4:D8
3	72	6160	32:Q8	3^2:Q8
5	20	22176	5:4	5:4
7	21	21120	7:3	7:3
11	55	8064	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:

58 available

Group constructions in GAP:

AtlasGroup( "M22" ), AtlasStabilizer( "HS", "HSG1-p100B0" ), AtlasStabilizer( "M23", "M23G1-p23B0" ), AtlasStabilizer( "McL", "McLG1-p2025aB0" ), AtlasStabilizer( "McL", "McLG1-p2025bB0" ), AtlasStabilizer( "U6(2)", "U62G1-p20736aB0" ), AtlasStabilizer( "U6(2)", "U62G1-p20736bB0" ), AtlasStabilizer( "U6(2)", "U62G1-p20736cB0" ), AtlasSubgroup( "HS", 1 ), AtlasSubgroup( "M22.2", 1 ), AtlasSubgroup( "M23", 1 ), AtlasSubgroup( "McL", 2 ), AtlasSubgroup( "McL", 3 ), AtlasSubgroup( "U6(2)", 11 ), AtlasSubgroup( "U6(2)", 12 ), AtlasSubgroup( "U6(2)", 13 ), MathieuGroup( 22 ), PerfectGroup( 443520, 1 ), PrimitiveGroup( 22, 1 ), PrimitiveGroup( 77, 1 ), PrimitiveGroup( 176, 3 ), PrimitiveGroup( 231, 1 ), PrimitiveGroup( 330, 1 ), PrimitiveGroup( 616, 1 ), PrimitiveGroup( 672, 5 ), TransitiveGroup( 22, 38 )

Stored class fusions from this table:

2¹⁰:M₂₂', 2¹⁰:M₂₂, Fi₂₂, HS, M₂₂.2, M₂₃, M^cL, U₆(2)

Stored class fusions to this table:

2¹¹.M₂₂, 2.M₂₂, 2³.S₄v₁, 2³:L₃(2), 2⁴:3²:4, 2⁴:D₈, 2⁴:A₆, 2⁴:S₅, 2¹⁰:M₂₂', 2¹⁰:M₂₂, 2 × 2.M₂₂, 2 × 3.M₂₂, 2 × 6.M₂₂, 3.M₂₂, 3²:Q₈, 4.M₂₂, 5:4, 6.M₂₂, 7:3, 11:5, 12.M₂₂, (A₄ × 3):2, A₆.2₃, A₇, L₂(11), L₃(4), M₂₂C2A, NRS(M₂₂, [2⁶])

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