Finite Group Databasebeta

C22×#14582961 #25960315

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productC22×#14582961

Splittings

FittingC22×#97×C43 ⋊ C2
SylowC43 ⋊ C22×#433

Subgroups

subgroupG/H
centerC23×C4C22×D43
commutatorC22×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×#97×C43C2
socleC24×C43C22×C4
prime radicalC24×D43C2×C4
cosocleC2×C4×C43C25
hypercenterC22×#97D43
hypocenterC43C22×#433
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23×C4 ◁ C22×#97

2310 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, 1033286);