Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | C3×C3⋊#13133323 |
| unambiguous semidirect product | C3⋊(C3×#13133323) |
| Fitting, Hall | C32×C17×C25 ⋊ C4 |
| derived | C3×C17×C25 ⋊ C3×C4 |
| Hall | C17×C25 ⋊ C3×Dic3 |
| Hall | C32×C25 ⋊ #595 |
| Hall | C32×C17 ⋊ #1035 |
| Sylow | C25 ⋊ C3×C3⋊#595 |
| Sylow | C17 ⋊ C3×C3⋊#1035 |
| Sylow | C32 ⋊ #13133323 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2550 |
972 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 78);