Finite Group Databasebeta

C4×#14583329 #25249877

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

Aliases

direct productC4×#14583329

Splittings

FittingC4×#135×C43 ⋊ C2
SylowC43 ⋊ C4×#508

Subgroups

subgroupG/H
centerC42#10621882
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC4×#135×C43C2
socleC22×C43C22×D8
prime radicalC2×#14583329C2
cosocleC2×C8×C43C24
hypercenterC4×#135D43
hypocenterC43C4×#508
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C2×C42 ◁ C2×C4×C8 ◁ C4×#135

690 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322848);