Finite Group Databasebeta

C4×#14582680 #25011638

order11008
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#14582680

Splittings

FittingC4×M32×C43 ⋊ C2
SylowC43 ⋊ C4×#349

Subgroups

subgroupG/H
centerC42(C2×D43)⋊C4
commutatorC22×C43C2×C4×C8
FrattiniC22×C8C22×D43
FittingC4×M32×C43C2
socleC22×C43C2×C22⋊C8
prime radicalC23×D43C2×C8
cosocleC22×C8×C43C23
hypercenterC4×M32D43
hypocenterC43C4×#349
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C2×C4×C8 ◁ C4×M32

522 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, 84609);