Finite Group Databasebeta

C2×#19136833 #25251905

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#19136833

Splittings

FittingC2×C43×#358 ⋊ C2
SylowC43 ⋊ C2×#2243

Subgroups

subgroupG/H
centerC23D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#358C2
socleC23×C43C2×D8
prime radicalC22×D344C22
hypercenterC2×#358D43
hypocenterC43C2×#2243
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

634 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

976 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 324876);