Finite Group Databasebeta

C4×#14583342 #25249930

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

Aliases

direct productC4×#14583342

Splittings

FittingC4×M32×C43 ⋊ C2
SylowC43 ⋊ C4×#510

Subgroups

subgroupG/H
centerC2×C4C2×D344
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC4×M32×C43C2
socleC22×C43C22×D8
prime radicalC2×#13063347C22
cosocleC2×C8×C43C24
hypercenterC4×M32D43
hypocenterC43C4×#510
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×M32

674 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, 322901);