Finite Group Databasebeta

C22×#14582801 #25254949

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210×C4

Aliases

direct productC22×#14582801

Splittings

FittingC23×C42×C43 ⋊ C2
SylowC43 ⋊ C22×#390

Subgroups

subgroupG/H
centerC25C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC23×C42×C43C2
socleC25×C43C23
prime radicalC24×D172C2
cosocleC23×C43C25
hypercenterC23×C42D43
hypocenterC43C22×#390
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C25 ◁ C23×C42

9534 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 327920);