Finite Group Databasebeta

C22×#14583161 #25963969

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

Aliases

direct productC22×#14583161

Splittings

FittingC22×#100×C43 ⋊ C2
SylowC43 ⋊ C22×#471

Subgroups

subgroupG/H
centerC23#13063298
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#100×C43C2
socleC23×C43#121
prime radicalC22×#13063351C2
hypercenterC22×#100D43
hypocenterC43C22×#471
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#100

2758 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1036940);