Finite Group DatabasebetaFinite Group Databasebeta| order | 12060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C67⋊C9)⋊Dic5 |
| unambiguous semidirect product | Dic335⋊C9 |
| derived, Hall | C5×C67 ⋊ C4×C9 |
| Hall | C5×C67⋊C9 ⋊ C4 |
| Hall | Dic335 ⋊ C9 |
| Hall | C67⋊C9 ⋊ Dic5 |
| Sylow | C67 ⋊ C9×Dic5 |
| Sylow | C5 ⋊ Dic67⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | C5⋊(D67⋊C3) |
| commutator, hypocenter | C5×C67 | C4×C9 |
| Fitting, socle, prime radical, cosocle | C2×C3×C5×C67 | C2×C3 |
| LCS | G ▷ C5×C67 | |
| UCS | C1 ◁ C2×C3 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,67,2,3|a^2=e,b^3=f,c^a=c^4,d^a=d^66,d^b=d^37402 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12060, 12);