Finite Group Databasebeta

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C22×C4×#11715871 #27136319

order12352
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC22×C4×#11715871
unambiguous semidirect productD193⋊(C2×C42)

Splittings

FittingC22×C4×C193 ⋊ C4
derived, SylowC193 ⋊ C22×C42

Subgroups

subgroupG/H
center, hypercenterC22×C4#11715871
commutator, hypocenterC193C22×C42
FrattiniC2C23×#11715871
FittingC22×C4×C193C4
socleC23×C193C2×C4
prime radicalC23×D193C22
cosocleC2×D193C24
LCSG ▷ C193
UCSC1 ◁ C22×C4

498 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

832 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 1609);