Finite Group DatabasebetaFinite Group Databasebeta| order | 12060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C67⋊#4379 |
| Fitting, socle, derived, Hall | C32×C5×C67 ⋊ C4 |
| Hall | C32×C67 ⋊ Dic5 |
| Hall | C5×C67 ⋊ #157 |
| Sylow | C67 ⋊ #4379 |
| Hall | C32×C5 ⋊ Dic67 |
| Sylow | C32 ⋊ Dic335 |
| Sylow | C5 ⋊ C67⋊#157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C5×C67 | C4 |
| prime radical, cosocle | C5×C3⋊D3×C67 | C2 |
| LCS | G ▷ C32×C5×C67 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,3^2,5,67|a^2=b,c^a=cd,d^a=cd^2,e^a=e^4,f^a=f^66,c^b=c^2,d^b=d^21008 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12060, 115);