Finite Group Databasebeta

C4×#14582865 #25094126

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

Aliases

direct productC4×#14582865

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ C4×#408

Subgroups

subgroupG/H
centerC2×C42C22×D43
commutatorC22×C43C22×C42
FrattiniC22×C4C23×D43
FittingC22×C4×C8×C43C2
socleC23×C43C23×C4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C4×#408
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C22×C4×C8

1662 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, 167097);