Finite Group Databasebeta

C4×#14583500 #25255698

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct productC4×#14583500

Splittings

FittingC42×D4×C43 ⋊ C2
SylowC43 ⋊ C4×#540

Subgroups

subgroupG/H
centerC22×C4C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC42×D4×C43C2
socle, cosocleC23×C43C25
prime radicalC2×#14583500C2
hypercenterC42×D4D43
hypocenterC43C4×#540
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C42×D4

2518 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, 328669);