Finite Group Databasebeta

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C2×C4×#13095402 #27136369

order12352
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C4×#13095402
unambiguous semidirect product#11715871⋊(C2×C8)

Splittings

FittingC2×C4×C193 ⋊ C8
derived, SylowC193 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4#13095402
commutator, hypocenterC193C2×C4×C8
FrattiniC2C22×#13095402
FittingC2×C4×C193C8
socleC22×C193C2×C8
prime radicalC22×D193C2×C4
cosocleC2×#11715871C23
LCSG ▷ C193
UCSC1 ◁ C2×C4

162 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

256 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 1659);