Finite Group Databasebeta

C2×#19136534 #25250365

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19136534

Splittings

FittingC22×Q32×C43 ⋊ C2
SylowC43 ⋊ C2×#2189

Subgroups

subgroupG/H
centerC23D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC22×Q32×C43C2
socleC23×C43C2×D8
prime radicalC22×#13063348C2
hypercenterC22×Q32D43
hypocenterC43C2×#2189
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

1146 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

982 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 323336);