Finite Group Databasebeta

C2×#19136517 #25250357

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

Aliases

direct productC2×#19136517

Splittings

FittingC22×SD32×C43 ⋊ C2
SylowC43 ⋊ C2×#2186

Subgroups

subgroupG/H
centerC23D8×D43
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
FittingC22×SD32×C43C2
socleC23×C43C2×D8
hypercenterC22×SD32D43
hypocenterC43C2×#2186
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×SD32

1198 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, 323328);