Finite Group Databasebeta

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C2×C22⋊#13095393 #27135220

order12352
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×C22⋊#13095393

Splittings

SylowC193 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C2×D193
commutatorC2×C193C22×C8
FrattiniC2×C4C22×D193
FittingC23×C4×C193C2
socleC23×C193C2×C4
prime radicalC24×C193C4
cosocleC2×C4×C193C23
hypercenterC23×C4D193
hypocenterC193C2×C22⋊C8
LCSG ▷ C2×C193 ▷ C193
UCSC1 ◁ C22×C4 ◁ C23×C4

202 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3112 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12352, 510);