Finite Group Databasebeta

C22×#14583055 #25962909

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

Aliases

direct productC22×#14583055

Splittings

SylowC43 ⋊ C22×#451

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC24×Q8×C43C2
socleC24×C43C2×D4
prime radicalC25×C43D4
hypercenterC24×Q8D43
hypocenterC43C22×#451
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C24×Q8

4982 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, 1035880);