Finite Group Databasebeta

C22×#14583085 #25963309

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

Aliases

direct productC22×#14583085

Splittings

FittingC22×#120×C43 ⋊ C2
SylowC43 ⋊ C22×B(4,𝔽2)

Subgroups

subgroupG/H
centerC23#13063293
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×#120×C43C2
socleC23×C43#120
hypercenterC22×#120D43
hypocenterC43C22×B(4,𝔽2)
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C22×#120

7014 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, 1036280);