Finite Group DatabasebetaFinite Group Databasebeta| order | 16119 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C199⋊C3)⋊C27 |
| derived, Sylow | C199 ⋊ C3×C27 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #13184226 |
| commutator, hypocenter | C199 | C3×C27 |
| Frattini | C3 | C3×#13184226 |
| Fitting | C9×C199 | C9 |
| socle | C3×C199 | C3×C9 |
| prime radical | C3×C199⋊C3 | C9 |
| cosocle | #13184224 | C32 |
| LCS | G ▷ C199 | |
| UCS | C1 ◁ C9 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5373 |
Polycyclic presentation:
3^4,199|a^3=c,c^3=d,e^a=e^175,e^b=e^92,e^c=e^106279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16119, 56);