Finite Group Databasebeta

C3×#21419371 #36382871

order22599
automorphism?
homologyAbelianization (H1) = C33×C9 · Schur multiplier (H2) = C35

Aliases

direct productC3×#21419371

Splittings

SylowC31 ⋊ C3×#6903

Subgroups

subgroupG/H
centerC3×C9C32×C31⋊C3
commutatorC3×C31C33×C9
FrattiniC9C33×C31⋊C3
FittingC3×C31×#737C3
socleC32×C31C32×C9
prime radicalC3×H(3,𝔽3)×C31C9
cosocleC9×C31C34
hypercenterC3×#737C31⋊C3
hypocenterC31C3×#6903
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C3×C9 ◁ C3×#737

848 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

Conjugacy classes & character table

1287 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 3892);