Finite Group DatabasebetaFinite Group Databasebeta| order | 3159 |
| automorphism | ? |
| homology | Abelianization (H1) = C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C33⋊C13)⋊C9 |
| derived | C33⋊C13 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | (C33⋊C13)⋊C3 |
| commutator, hypocenter | C33⋊C13 | C9 |
| Fitting, socle | C34 | C13⋊C3 |
| prime radical, cosocle | C3×C33⋊C13 | C3 |
| LCS | G ▷ C33⋊C13 | |
| UCS | C1 ◁ C3 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 117 |
Polycyclic presentation:
3,13,3^4|a^3=f,b^a=b^3,c^a=cde,d^a=de^2,c^b=cd,d^b=de,e^b=c^2e^239 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3159, 312);