Finite Group Databasebeta

C4×#14582915 #25094323

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

Aliases

direct productC4×#14582915

Splittings

FittingC2×C4×M16×C43 ⋊ C2
SylowC43 ⋊ C4×#421

Subgroups

subgroupG/H
centerC42C2×C22⋊D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC2×C4×M16×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×C4×M16D43
hypocenterC43C4×#421
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×C4×M16

1618 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 167294);