Finite Group Databasebeta

C2×#19135655 #25123598

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C27

Aliases

direct productC2×#19135655

Splittings

FittingC2×C43×#536 ⋊ C2
SylowC43 ⋊ C2×#2009

Subgroups

subgroupG/H
centerC22#14582807
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#536C2
socleC22×C43#392
prime radicalC2×#14583697C2
hypercenterC2×#536D43
hypocenterC43C2×#2009
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#536

1926 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

970 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 196569);