Finite Group Databasebeta

C32×#14578896 #36382882

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

Aliases

direct productC32×#14578896

Splittings

SylowC31 ⋊ C32×#731

Subgroups

subgroupG/H
centerC33C32⋊(C31⋊C3)
commutator, cosocleC32×C31C34
FrattiniC32C33×C31⋊C3
Fitting, prime radicalC32×H(3,𝔽3)×C31C3
socleC33×C31H(3,𝔽3)
hypercenterC32×H(3,𝔽3)C31⋊C3
hypocenterC31C32×#731
LCSG ▷ C32×C31 ▷ C3×C31 ▷ C31
UCSC1 ◁ C33 ◁ C34 ◁ C32×H(3,𝔽3)

1160 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, 3903);