Finite Group Databasebeta

C3×#21419215 #36380050

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

Aliases

direct productC3×#21419215

Splittings

SylowC31 ⋊ C3×#6861

Subgroups

subgroupG/H
centerC33C32⋊(C31⋊C3)
commutator, cosocleC33×C31C33
FrattiniC33C32×C31⋊C3
FittingC3×C31×C32⋊C9C3
socleC33×C31H(3,𝔽3)
prime radicalC34×C31C32
hypercenterC3×C32⋊C9C31⋊C3
hypocenterC31C3×#6861
LCSG ▷ C33×C31 ▷ C32×C31 ▷ C31
UCSC1 ◁ C33 ◁ C34 ◁ C3×C32⋊C9

284 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

Conjugacy classes & character table

1095 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 1071);