Finite Group Databasebeta

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C23×#11744762 #20299721

order7232
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC23×#11744762

Splittings

Fitting, socleC23×C113 ⋊ C8
derived, SylowC113 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC23#11744762
commutator, hypocenterC113C23×C8
FrattiniC1G
Fitting, socleC23×C113C8
LCSG ▷ C113
UCSC1 ◁ C23

338 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×(C2×#11744762)⋊C4, C22⋊C4×#11744762, #28407719, …
maximal normal subgroup ofC2×(C2×#11744762)⋊C4, C22⋊C4×#11744762, #28407719, …
maximal quotient ofC22×C4×#11744762, C22×C22⋊#11744762, C22×C4⋊#11744762, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7232, 1672);