Finite Group Databasebeta

C9×#14578902 #36381141

order22599
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C33

Aliases

direct productC9×#14578902

Splittings

SylowC31 ⋊ C9×#733

Subgroups

subgroupG/H
centerC3×C9C32⋊(C31⋊C3)
commutatorC32×C31C32×C9
FrattiniC33C32×C31⋊C3
FittingC3×C92×C31C3
socleC32×C31C3×H(3,𝔽3)
prime radical, cosocleC33×C31C33
hypercenterC3×C92C31⋊C3
hypocenterC31C9×#733
LCSG ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C3×C9 ◁ C32×C9 ◁ C3×C92

274 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

Conjugacy classes & character table

2583 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 2162);