Finite Group Databasebeta

C22×#14582637 #25063680

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC22×#14582637

Splittings

SylowC43 ⋊ C22×#328

Subgroups

subgroupG/H
centerC24(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×C22⋊C8×C43C2
socleC24×C43C22⋊C4
prime radicalC25×C43D4
cosocleC22×C4×C43C24
hypercenterC22×C22⋊C8D43
hypocenterC43C22×#328
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

1846 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 136651);