Finite Group Databasebeta

C31⋊C3×#6913 #36382920

order22599
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C36

Aliases

direct productC31⋊C3×#6913

Splittings

FittingC31×#6913 ⋊ C3
SylowC31 ⋊ C3×#6913

Subgroups

subgroupG/H
centerC3C3×H(3,𝔽3)×C31⋊C3
commutator, cosocleC32×C31C34
FrattiniC32C33×C31⋊C3
FittingC31×#6913C3
socleC3×C31C32×H(3,𝔽3)
hypercenter#6913C31⋊C3
hypocenterC31C3×#6913
LCSG ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C3 ◁ C3×C9 ◁ #6913

992 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, 3941);