Finite Group DatabasebetaFinite Group Databasebeta| order | 36060 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×#14558894⋊C5 |
| unambiguous semidirect product | (C3×#14558894)⋊C5 |
| Fitting, socle, Hall | C3×C601 ⋊ C4×C5 |
| derived, Sylow | C601 ⋊ C3×C4×C5 |
| Hall | C3×C601⋊C5 ⋊ C4 |
| Hall | C3×#14558894 ⋊ C5 |
| Hall | C601⋊C5 ⋊ C3×C4 |
| Hall | #14558894 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #14558894⋊C5 |
| commutator, hypocenter | C601 | C3×C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C601 | C4×C5 |
| prime radical | C3×D601⋊C5 | C2 |
| cosocle | D601 | C2×C3×C5 |
| LCS | G ▷ C601 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1803 |
150 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36060, 22);