Finite Group Databasebeta

C22×#14583341 #26003096

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC22×#14583341

Splittings

FittingC22×Q32×C43 ⋊ C2
SylowC43 ⋊ C22×#510

Subgroups

subgroupG/H
centerC23D8×D43
commutator, cosocleC8×C43C25
FrattiniC8C24×D43
FittingC22×Q32×C43C2
socleC23×C43C2×D8
prime radicalC22×#13063348C2
hypercenterC22×Q32D43
hypocenterC43C22×#510
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×Q32

2078 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1076067);