Finite Group Databasebeta

C3×#21419281 #36382124

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

Aliases

direct productC3×#21419281

Splittings

FittingC3×C31×C9⋊C9 ⋊ C3
SylowC31 ⋊ C3×#6883

Subgroups

subgroupG/H
centerC32#14578900
commutator, cosocleC3×C9×C31C33
FrattiniC3×C9C32×C31⋊C3
FittingC3×C31×C9⋊C9C3
socleC32×C31#732
prime radicalC3×#14578900C3
hypercenterC3×C9⋊C9C31⋊C3
hypocenterC31C3×#6883
LCSG ▷ C3×C9×C31 ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C32 ◁ C33 ◁ C32×C9 ◁ C3×C9⋊C9

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2511

Conjugacy classes & character table

1047 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 3145);