Finite Group Databasebeta

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C22×C4⋊#11715871 #27136321

order12352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

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

Splittings

FittingC22×C4×C193 ⋊ C4
SylowC193 ⋊ C22×C4⋊C4

Subgroups

subgroupG/H
centerC23C2×#11715871
commutatorC2×C193C23×C4
FrattiniC2C23×#11715871
FittingC22×C4×C193C4
socleC23×C193C2×C4
prime radicalC23×D193C22
cosocleC2×D193C24
hypercenterC22×C4#11715871
hypocenterC193C22×C4⋊C4
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C23 ◁ C22×C4

418 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

808 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 1611);