Finite Group Databasebeta

C4×#14582713 #25011851

order11008
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#14582713

Splittings

FittingC4×M32×C43 ⋊ C2
SylowC43 ⋊ C4×#361

Subgroups

subgroupG/H
centerC2×C4#13063247
commutatorC8×C43C2×C42
FrattiniC22×C8C22×D43
FittingC4×M32×C43C2
socleC22×C43C2×#102
prime radicalC22×D344C22
cosocleC22×C8×C43C23
hypercenterC4×M32D43
hypocenterC43C4×#361
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×M32

498 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 84822);