Finite Group Databasebeta

C22×#14582882 #25960086

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#14582882

Splittings

FittingC22×#101×C43 ⋊ C2
SylowC43 ⋊ C22×#413

Subgroups

subgroupG/H
centerC23C22⋊C4×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×#101×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC23×#10621902C2
cosocleC2×C4×C43C25
hypercenterC22×#101D43
hypocenterC43C22×#413
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#101

5118 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033057);