Finite Group Databasebeta

C22×#14582746 #25254769

order11008
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4

Aliases

direct productC22×#14582746

Splittings

FittingC22×#95×C43 ⋊ C2
SylowC43 ⋊ C22×C4×C22⋊C4

Subgroups

subgroupG/H
centerC25C22×D43
commutatorC2×C43C23×C42
FrattiniC23C24×D43
FittingC22×#95×C43C2
socleC25×C43C23
prime radicalC25×D43C22
cosocleC23×C43C25
hypercenterC22×#95D43
hypocenterC43C22×C4×C22⋊C4
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C25 ◁ C22×#95

9534 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 327740);