Finite Group Databasebeta

C2×#19136719 #25251159

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

Aliases

direct productC2×#19136719

Splittings

FittingC2×C43×#362 ⋊ C2
SylowC43 ⋊ C2×#2222

Subgroups

subgroupG/H
centerC22#14583134
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC2×C43×#362C2
socleC22×C43#466
prime radicalC2×#10621898D4
hypercenterC2×#362D43
hypocenterC43C2×#2222
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#362

638 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

724 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 324130);