Finite Group Databasebeta

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C22×C4×#90673 #20299658

order7232
isoclinismisoclinic class of #90673
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C4×#90673
unambiguous semidirect productD113⋊(C2×C42)

Splittings

FittingC22×C4×C113 ⋊ C4
derived, SylowC113 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC22×C4#90673
commutator, hypocenterC113C22×C42
FrattiniC2C23×#90673
FittingC22×C4×C113C4
socleC23×C113C2×C4
LCSG ▷ C113
UCSC1 ◁ C22×C4

498 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

512 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#95×#90673, C4×(C2×#90673)⋊C4, #28405749, …
maximal normal subgroup of#95×#90673, C4×(C2×#90673)⋊C4, #28405749, …
maximal quotient ofC2×C42×#90673, C22×(C2×#90673)⋊C4, C2×#20299534, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7232, 1609);