Finite Group Databasebeta

C22×#14583196 #25964063

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC22×#14583196

Splittings

FittingC22×#125×C43 ⋊ C2
SylowC43 ⋊ C22×#478

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#125×C43C2
socleC24×C43C2×D4
prime radicalC23×D172C22
hypercenterC22×#125D43
hypocenterC43C22×#478
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#125

2574 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1037034);