Finite Group Databasebeta

C22×#14583020 #25960893

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#14583020

Splittings

FittingC22×#108×C43 ⋊ C2
SylowC43 ⋊ C22×#444

Subgroups

subgroupG/H
centerC22×C4D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×#108×C43C2
socleC23×C43C4×D4
prime radicalC22×#13063347C2
cosocleC2×C4×C43C25
hypercenterC22×#108D43
hypocenterC43C22×#444
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#108

2710 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, 1033864);