Finite Group DatabasebetaFinite Group Databasebeta| order | 36060 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | Dic3×C601⋊C5 |
| unambiguous semidirect product | C3⋊(C4×C601⋊C5) |
| unambiguous semidirect product | (Dic3×C601)⋊C5 |
| derived, Hall | C3×C601 ⋊ C4×C5 |
| Hall | C3×C601⋊C5 ⋊ C4 |
| Hall | Dic3×C601 ⋊ C5 |
| Sylow | C601 ⋊ C5×Dic3 |
| Sylow | C3 ⋊ C4×C601⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×C601⋊C5 |
| commutator, hypocenter | C3×C601 | C4×C5 |
| Fitting, socle, cosocle | C2×C3×C601 | C2×C5 |
| prime radical | C2×C3×C601⋊C5 | C2 |
| LCS | G ▷ C3×C601 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7212 |
750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36060, 13);