Finite Group DatabasebetaFinite Group Databasebeta| order | 36060 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (Dic601⋊C3)⋊C5 |
| unambiguous semidirect product | (Dic601⋊C5)⋊C3 |
| derived, Sylow | C601 ⋊ C3×C4×C5 |
| Hall | Dic601⋊C5 ⋊ C3 |
| Hall | (C601⋊C3)⋊C5 ⋊ C4 |
| Hall | Dic601⋊C3 ⋊ C5 |
| Hall | C601⋊C5 ⋊ C3×C4 |
| Hall | Dic601 ⋊ C3×C5 |
| Hall | C601⋊C3 ⋊ C4×C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (D601⋊C3)⋊C5 |
| commutator, hypocenter | C601 | C3×C4×C5 |
| Fitting, socle, cosocle | C2×C601 | C2×C3×C5 |
| prime radical | C2×(C601⋊C3)⋊C5 | C2 |
| LCS | G ▷ C601 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2404 |
Polycyclic presentation:
2,3,5,601,2|a^2=e,d^a=d^600,d^b=d^576,d^c=d^423100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36060, 18);