Finite Group Databasebeta

C22×#14583166 #25963975

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#14583166

Splittings

FittingC23×D8×C43 ⋊ C2
SylowC43 ⋊ C22×#472

Subgroups

subgroupG/H
centerC23#13063296
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC23×D8×C43C2
socleC23×C43#121
hypercenterC23×D8D43
hypocenterC43C22×#472
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×D8

2886 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1036946);