Finite Group Databasebeta

C22×#14582682 #25249293

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#14582682

Splittings

FittingC23×C16×C43 ⋊ C2
SylowC43 ⋊ C22×#350

Subgroups

subgroupG/H
centerC22×C8D172
commutatorC4×C43C23×C8
FrattiniC2×C8C23×D43
FittingC23×C16×C43C2
socleC23×C43C22⋊C8
prime radicalC22×#10621898C4
cosocleC2×C8×C43C24
hypercenterC23×C16D43
hypocenterC43C22×#350
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C23×C8 ◁ C23×C16

1174 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, 322264);