Finite Group Databasebeta

C22×#14582789 #25254923

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29×C4

Aliases

direct productC22×#14582789

Splittings

FittingC23×C4⋊C4×C43 ⋊ C2
SylowC43 ⋊ C22×#388

Subgroups

subgroupG/H
centerC25C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC23×C4⋊C4×C43C2
socleC25×C43C23
prime radicalC25×D43C22
cosocleC23×C43C25
hypercenterC23×C4⋊C4D43
hypocenterC43C22×#388
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C25 ◁ C23×C4⋊C4

5966 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 327894);