Finite Group Databasebeta

C3×#11760452 #15691691

order3159
automorphism?
homologyAbelianization (H1) = C34 · Schur multiplier (H2) = C35

Aliases

direct productC3×#11760452

Splittings

SylowC13 ⋊ C3×#737

Subgroups

subgroupG/H
centerC32C32×C13⋊C3
commutator, cosocleC3×C13C34
FrattiniC3C33×C13⋊C3
Fitting, prime radicalC3×C13×H(3,𝔽3)C3
socleC32×C13C33
hypercenterC3×H(3,𝔽3)C13⋊C3
hypocenterC13C3×#737
LCSG ▷ C3×C13 ▷ C13
UCSC1 ◁ C32 ◁ C3×H(3,𝔽3)

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1053

Conjugacy classes & character table

231 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3159, 301);