Finite Group Databasebeta

C22×#14583007 #25960637

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

Aliases

direct productC22×#14583007

Splittings

SylowC43 ⋊ C22×#441

Subgroups

subgroupG/H
centerC24C2×D172
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×#97×C43C2
socle, prime radicalC24×C43C2×D4
cosocleC2×C4×C43C25
hypercenterC22×#97D43
hypocenterC43C22×#441
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#97

2790 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, 1033608);