Finite Group Databasebeta

C2×#19133747 #25072303

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

Aliases

direct productC2×#19133747

Splittings

FittingC2×C43×#332 ⋊ C2
SylowC43 ⋊ C2×#1635

Subgroups

subgroupG/H
centerC23#13063295
commutator, cosocleC42×C43C24
FrattiniC42C23×D43
FittingC2×C43×#332C2
socleC23×C43#120
prime radicalC2×#14583552C2
hypercenterC2×#332D43
hypocenterC43C2×#1635
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

1206 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

850 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 145274);