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C22×ΓL(1,𝔽8)×C113 #23748803

order9492
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C22×C3×C113 · Schur multiplier (H2) = C2

Aliases

direct productC22×ΓL(1,𝔽8)×C113

Splittings

Fitting, socle, HallC22×C7×C113 ⋊ C3
derived, SylowC7 ⋊ C22×C3×C113
HallC7×C113 ⋊ C22×C3
HallC22×C7 ⋊ C3×C113

Subgroups

subgroupG/H
center, hypercenterC22×C113ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C22×C3×C113
FrattiniC1G
Fitting, socleC22×C7×C113C3
LCSG ▷ C7
UCSC1 ◁ C22×C113

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2260 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofA4×ΓL(1,𝔽8)×C113, C2×D3×ΓL(1,𝔽8)×C113, C22×C3×ΓL(1,𝔽8)×C113
maximal normal subgroup ofA4×ΓL(1,𝔽8)×C113, C22×C3×ΓL(1,𝔽8)×C113
maximal quotient ofC22×C7⋊C9×C113, C2×D3×ΓL(1,𝔽8)×C113, C22×C3×ΓL(1,𝔽8)×C113

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9492, 45);