Finite Group Databasebeta

C22×#14582892 #25960112

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#14582892

Splittings

FittingC22×#102×C43 ⋊ C2
SylowC43 ⋊ C22×#416

Subgroups

subgroupG/H
centerC24D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×#102×C43C2
socleC24×C43C2×D4
prime radicalC23×#10621900C2
cosocleC2×C4×C43C25
hypercenterC22×#102D43
hypocenterC43C22×#416
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

5326 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033083);