Finite Group DatabasebetaFinite Group Databasebeta| order | 36300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C11 |
| direct product | C3×C5×#14559075 |
| Fitting, socle | C3×C5×C112 ⋊ Dic5 |
| derived | #10597245 ⋊ C3×C4×C5 |
| Hall | C3×C5×#10597245 ⋊ C4 |
| Hall | C5×#10597245 ⋊ C3×C4 |
| Hall | C3×C112 ⋊ C5×Dic5 |
| Sylow | C112 ⋊ C3×C5×Dic5 |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 330 |
210 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36300, 501);