Finite Group Databasebeta

C22×#14582853 #25959987

order11008
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC22×#14582853

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ C22×#405

Subgroups

subgroupG/H
centerC23×C8C2×D43
commutatorC2×C43C23×C42
FrattiniC2×C4C24×D43
FittingC22×C4×C8×C43C2
socleC24×C43C22×C4
prime radicalC24×D43C2×C4
cosocleC2×C4×C43C25
hypercenterC22×C4×C8D43
hypocenterC43C22×#405
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C8 ◁ C22×C4×C8

3518 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2848 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1032958);