Finite Group Databasebeta

C2×#19133991 #25078857

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19133991

Splittings

FittingC2×C43×#500 ⋊ C2
SylowC43 ⋊ C2×#1675

Subgroups

subgroupG/H
centerC23#13063296
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#500C2
socleC23×C43#121
prime radicalC22×D172D4
hypercenterC2×#500D43
hypocenterC43C2×#1675
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

726 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

982 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 151828);