Finite Group Databasebeta

C4×#14583001 #25095093

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#14583001

Splittings

FittingC4×#97×C43 ⋊ C2
SylowC43 ⋊ C4×#440

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC4×#97×C43C2
socleC23×C43C22×D4
prime radicalC22×D172C23
cosocleC22×C4×C43C24
hypercenterC4×#97D43
hypocenterC43C4×#440
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C43 ◁ C4×#97

1206 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, 168064);