Finite Group Databasebeta

C22×#14582863 #25960028

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

Aliases

direct productC22×#14582863

Splittings

SylowC43 ⋊ C22×#407

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC25×C4×C43C2
socleC24×C43C22×C4
prime radicalC26×C43C4
cosocleC2×C4×C43C25
hypercenterC25×C4D43
hypocenterC43C22×#407
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C25×C4

7214 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, 1032999);