Finite Group Databasebeta

C22×#14583094 #25963373

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC22×#14583094

Splittings

FittingC22×C4×D4×C43 ⋊ C2
SylowC43 ⋊ C22×#459

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×C4×D4×C43C2
socleC24×C43C2×D4
hypercenterC22×C4×D4D43
hypocenterC43C22×#459
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×D4

3910 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1036344);