Finite Group Databasebeta

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C2×C4⋊#13095400 #27136259

order12352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4⋊#13095400

Splittings

SylowC193 ⋊ C2×C4⋊C8

Subgroups

subgroupG/H
centerC23C2×#11715871
commutatorC2×C193C22×C8
FrattiniC22C22×#11715871
FittingC22×C4×C193C4
socle, prime radicalC23×C193C2×C4
cosocleC2×Dic193C23
hypercenterC22×C4#11715871
hypocenterC193C2×C4⋊C8
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C23 ◁ C22×C4

138 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, 1549);