Finite Group Databasebeta

C22×#14583017 #25960889

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC22×#14583017

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ C22×#443

Subgroups

subgroupG/H
centerC22×C8D172
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×C4×C8×C43C2
socleC23×C43C4×D4
prime radicalC22×#13063347C2
cosocleC2×C4×C43C25
hypercenterC22×C4×C8D43
hypocenterC43C22×#443
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C22×C4×C8

2750 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033860);