Finite Group Databasebeta

C31⋊C3×#6879 #36382075

order22599
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33×C9

Aliases

direct productC31⋊C3×#6879

Splittings

FittingC31×#6879 ⋊ C3
SylowC31 ⋊ C3×#6879

Subgroups

subgroupG/H
centerC3#732×C31⋊C3
commutator, cosocleC3×C9×C31C33
FrattiniC3×C9C32×C31⋊C3
FittingC31×#6879C3
socleC3×C31C3×#732
hypercenter#6879C31⋊C3
hypocenterC31C3×#6879
LCSG ▷ C3×C9×C31 ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C3 ◁ C32 ◁ C3×C9 ◁ #6879

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 837

Conjugacy classes & character table

455 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 3096);