Finite Group Databasebeta

C2×#19136619 #25250764

order11008
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19136619

Splittings

FittingC2×C43×#454 ⋊ C2
SylowC43 ⋊ C2×#2204

Subgroups

subgroupG/H
centerC22#14583085
commutator, cosocleC2×Q8×C43C24
FrattiniC2×Q8C23×D43
FittingC2×C43×#454C2
socleC22×C43B(4,𝔽2)
hypercenterC2×#454D43
hypocenterC43C2×#2204
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ C2×#454

1200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

712 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 323735);