Finite Group DatabasebetaFinite Group Databasebeta| order | 16119 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Sylow | C199 ⋊ #737 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×C199⋊C3 |
| commutator, socle, cosocle | C3×C199 | C33 |
| Fitting, prime radical | H(3,𝔽3)×C199 | C3 |
| hypercenter | H(3,𝔽3) | C199⋊C3 |
| hypocenter | C199 | #737 |
| LCS | G ▷ C3×C199 ▷ C199 | |
| UCS | C1 ◁ C3 ◁ H(3,𝔽3) | |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5373 |
Polycyclic presentation:
3^4,199|c^3=d,b^a=bd,e^c=e^106759 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16119, 46);