Finite Group Databasebeta

C4×#14583341 #25249927

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC4×#14583341

Splittings

FittingC4×Q32×C43 ⋊ C2
SylowC43 ⋊ C4×#510

Subgroups

subgroupG/H
centerC2×C4D8×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC4×Q32×C43C2
socleC22×C43C22×D8
prime radicalC2×#13063348C22
cosocleC2×C8×C43C24
hypercenterC4×Q32D43
hypocenterC43C4×#510
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×C8 ◁ C4×Q32

674 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322898);