Finite Group Databasebeta

C4×#14582896 #25094349

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#14582896

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ C4×#416

Subgroups

subgroupG/H
centerC2×C42D172
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC22×C4×C8×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C4×#416
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C22×C4×C8

1670 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, 167320);