Finite Group Databasebeta

C3×#21419228 #36380973

order22599
automorphism?
homologyAbelianization (H1) = C32×C9 · Schur multiplier (H2) = C34

Aliases

direct productC3×#21419228

Splittings

SylowC31 ⋊ C3×#6867

Subgroups

subgroupG/H
centerC33C32⋊(C31⋊C3)
commutatorC32×C31C32×C9
FrattiniC33C32×C31⋊C3
FittingC33×C9×C31C3
socleC33×C31H(3,𝔽3)
prime radicalC34×C31C32
cosocleC33×C31C33
hypercenterC33×C9C31⋊C3
hypocenterC31C3×#6867
LCSG ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C33 ◁ C34 ◁ C33×C9

476 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, 1994);