Finite Group Databasebeta

C22×#14582778 #25254910

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C212

Aliases

direct productC22×#14582778

Splittings

FittingC25×C4×C43 ⋊ C2
SylowC43 ⋊ C22×#386

Subgroups

subgroupG/H
centerC25C22×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC25×C4×C43C2
socleC25×C43C23
prime radicalC24×C22⋊D43C2
cosocleC23×C43C25
hypercenterC25×C4D43
hypocenterC43C22×#386
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C25 ◁ C25×C4

11630 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 327881);