Finite Group Databasebeta

← Prev (#15691655) Next (#15691657) →

#15691656

order3159
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

No aliases for this group.

Splittings

FittingC3×C13×H(3,𝔽3) ⋊ C3
SylowC13 ⋊ #6909

Subgroups

subgroupG/H
centerC3C3×C32⋊(C13⋊C3)
commutator, cosocleC32×C13C33
FrattiniC32C32×C13⋊C3
FittingC3×C13×H(3,𝔽3)C3
socleC3×C13C3×H(3,𝔽3)
hypercenterC3×H(3,𝔽3)C13⋊C3
hypocenterC13#6909
LCSG ▷ C32×C13 ▷ C3×C13 ▷ C13
UCSC1 ◁ C3 ◁ C33 ◁ C3×H(3,𝔽3)

148 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 351

Polycyclic presentation:

3^5,13|b^a=bd,d^a=de,f^a=f^3,c^b=ce

Conjugacy classes & character table

167 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3159, 266);