Finite Group DatabasebetaFinite Group Databasebeta| order | 14661 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C9×C181 ⋊ C9 |
| Sylow | C181 ⋊ C9⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C3×#13108658 |
| commutator, socle | C3×C181 | C3×C9 |
| Fitting | C9×C181 | C9 |
| prime radical, cosocle | C3×C181⋊C3 | C32 |
| hypercenter | C9 | #13108658 |
| hypocenter | C181 | C9⋊C9 |
| LCS | G ▷ C3×C181 ▷ C181 | |
| UCS | C1 ◁ C3 ◁ C9 | |
34 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1629 |
Polycyclic presentation:
3^4,181|a^3=d,b^3=c,b^a=bc,e^a=e^39,e^d=e^132213 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14661, 54);