Finite Group Databasebeta

C22×#14582701 #25249470

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC22×#14582701

Splittings

FittingC23×C16×C43 ⋊ C2
SylowC43 ⋊ C22×#357

Subgroups

subgroupG/H
centerC24D344
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC23×C16×C43C2
socleC24×C43D8
prime radicalC23×D344C2
cosocleC2×C8×C43C24
hypercenterC23×C16D43
hypocenterC43C22×#357
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×C8 ◁ C23×C16

1470 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322441);