Finite Group Databasebeta

C22×C4×#10621882 #25960597

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

Aliases

direct productC22×C4×#10621882

Splittings

FittingC22×C4×D4×C43 ⋊ C2
SylowC43 ⋊ C22×C4×D8

Subgroups

subgroupG/H
centerC23×C4C22⋊D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×C4×D4×C43C2
socleC24×C43C2×D4
prime radicalC23×#10621882C2
cosocleC2×C4×C43C25
hypercenterC22×C4×D4D43
hypocenterC43C22×C4×D8
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×C42 ◁ C22×C4×D4

3694 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033568);