Finite Group Databasebeta

C22×#14583224 #25964335

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27×C4

Aliases

direct productC22×#14583224

Splittings

FittingC22×C22⋊C8×C43 ⋊ C2
SylowC43 ⋊ C22×#482

Subgroups

subgroupG/H
centerC24C2×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×C22⋊C8×C43C2
socleC24×C43C2×D4
prime radicalC22×#13063299C2
hypercenterC22×C22⋊C8D43
hypocenterC43C22×#482
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×C22⋊C8

2702 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, 1037306);