Finite Group Databasebeta

C22×#14583087 #25963311

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C211

Aliases

direct productC22×#14583087

Splittings

FittingC22×#99×C43 ⋊ C2
SylowC43 ⋊ C22×B(4,𝔽2)

Subgroups

subgroupG/H
centerC23#13063295
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×#99×C43C2
socleC23×C43#120
hypercenterC22×#99D43
hypocenterC43C22×B(4,𝔽2)
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C22×#99

7014 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, 1036282);