Finite Group Databasebeta

C22×#14582664 #25094014

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C27

Aliases

direct productC22×#14582664

Splittings

SylowC43 ⋊ C22×#341

Subgroups

subgroupG/H
centerC23×C4D172
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC24×C8×C43C2
socleC24×C43C4⋊C4
prime radicalC25×C43Q8
cosocleC22×C4×C43C24
hypercenterC24×C8D43
hypocenterC43C22×#341
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C24×C4 ◁ C24×C8

2238 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, 166985);