Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C25 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×#15690028 |
| unambiguous semidirect product | C3⋊(C22×#15690028) |
| unambiguous semidirect product | (C2×C3)⋊(C2×#15690028) |
| derived, Hall | C3×C112 ⋊ C22×C25 |
| Hall | C3×#15690028 ⋊ C22 |
| Hall | C2×D3×C112 ⋊ C25 |
| Sylow | C112 ⋊ C2×D3×C25 |
| Sylow | C3 ⋊ C22×#15690028 |
160 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1650 |
870 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 285);