Finite Group Databasebeta

C22×#14582899 #25960130

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

Aliases

direct productC22×#14582899

Splittings

FittingC22×#103×C43 ⋊ C2
SylowC43 ⋊ C22×#417

Subgroups

subgroupG/H
centerC24D4×D43
commutatorC4×C43C24×C4
FrattiniC2×C4C24×D43
FittingC22×#103×C43C2
socleC24×C43C2×D4
prime radicalC23×#10621902C2
cosocleC2×C4×C43C25
hypercenterC22×#103D43
hypocenterC43C22×#417
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#103

5502 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033101);