Finite Group Databasebeta

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C2×Q8×#11715871 #27136324

order12352
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×Q8×#11715871
unambiguous semidirect productD193⋊(C4×Q8)

Splittings

FittingC2×Q8×C193 ⋊ C4
SylowC193 ⋊ C2×C4×Q8

Subgroups

subgroupG/H
centerC22C22×#11715871
commutatorC2×C193C23×C4
FrattiniC2C23×#11715871
FittingC2×Q8×C193C4
socleC22×C193C22×C4
prime radicalC22×D193C23
cosocleC2×D193C24
hypercenterC2×Q8#11715871
hypocenterC193C2×C4×Q8
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C22 ◁ C2×Q8

298 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 1614);