Finite Group Databasebeta

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C22×#14268661 #20299730

order7232
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC22×#14268661

Splittings

Fitting, socleC22×C113 ⋊ C16
derived, SylowC113 ⋊ C22×C16

Subgroups

subgroupG/H
center, hypercenterC22#14268661
commutator, hypocenterC113C22×C16
FrattiniC1G
Fitting, socleC22×C113C16
LCSG ▷ C113
UCSC1 ◁ C22

98 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C2×#14268661)⋊C4, C2×C4×#14268661, C2×C22⋊#14268661, …
maximal normal subgroup of(C2×#14268661)⋊C4, C2×C4×#14268661, C2×C22⋊#14268661, …
maximal quotient ofC2×C4×#14268661, C2×C22⋊#14268661, C2×C4⋊#14268661, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7232, 1681);