Finite Group Databasebeta

C3×#21419320 #36382297

order22599
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C36

Aliases

direct productC3×#21419320

Splittings

SylowC31 ⋊ C3×#6893

Subgroups

subgroupG/H
centerC33C32×C31⋊C3
commutator, cosocleC32×C31C34
FrattiniC32C33×C31⋊C3
Fitting, prime radicalC32×H(3,𝔽3)×C31C3
socleC33×C31C33
hypercenterC32×H(3,𝔽3)C31⋊C3
hypocenterC31C3×#6893
LCSG ▷ C32×C31 ▷ C31
UCSC1 ◁ C33 ◁ C32×H(3,𝔽3)

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7533

Conjugacy classes & character table

1143 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22599, 3318);