Finite Group Databasebeta

C22×#14583223 #25964334

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

Aliases

direct productC22×#14583223

Splittings

FittingC22×#117×C43 ⋊ C2
SylowC43 ⋊ C22×#482

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#117×C43C2
socleC24×C43C2×D4
prime radicalC22×#13063299C2
hypercenterC22×#117D43
hypocenterC43C22×#482
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C22×#117

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, 1037305);