Finite Group Databasebeta

C22×#14582905 #25960121

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

Aliases

direct productC22×#14582905

Splittings

FittingC23×M16×C43 ⋊ C2
SylowC43 ⋊ C22×#418

Subgroups

subgroupG/H
centerC24C2×D172
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC23×M16×C43C2
socleC24×C43C2×D4
prime radicalC24×D172C2
cosocleC2×C4×C43C25
hypercenterC23×M16D43
hypocenterC43C22×#418
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×C4 ◁ C23×M16

7214 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033092);