Finite Group Databasebeta

C2×#19136366 #25249607

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19136366

Splittings

FittingC2×C43×#365 ⋊ C2
SylowC43 ⋊ C2×#2155

Subgroups

subgroupG/H
centerC22#106×D43
commutatorC8×C43C23×C4
FrattiniC2×C8C23×D43
FittingC2×C43×#365C2
socleC22×C43C2×#106
prime radicalC23×D43SD16
cosocleC2×C8×C43C24
hypercenterC2×#365D43
hypocenterC43C2×#2155
LCSG ▷ C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

658 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322578);