Finite Group Databasebeta

C3×#21419220 #36380943

order22599
automorphism?
homologyAbelianization (H1) = C3×C92 · Schur multiplier (H2) = C33

Aliases

direct productC3×#21419220

Splittings

SylowC31 ⋊ C3×#6864

Subgroups

subgroupG/H
centerC32×C9C3×C31⋊C3
commutatorC3×C31C3×C92
FrattiniC3×C9C32×C31⋊C3
FittingC32×C27×C31C3
socle, prime radicalC33×C31C3×C9
cosocleC3×C9×C31C33
hypercenterC32×C27C31⋊C3
hypocenterC31C3×#6864
LCSG ▷ C3×C31 ▷ C31
UCSC1 ◁ C32×C9 ◁ C32×C27

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 22599

Conjugacy classes & character table

2727 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 1964);