Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C4 · Schur multiplier (H2) = C3 |
| direct product | C32×#13133322 |
| Fitting, Hall | C32×C17×C25 ⋊ C4 |
| derived, Hall | C17×C25 ⋊ C32×C4 |
| Hall | C32×C25 ⋊ Dic17 |
| Hall | C32×C17 ⋊ #1035 |
| Sylow | C25 ⋊ C32×Dic17 |
| Sylow | C17 ⋊ C32×#1035 |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3825 |
1098 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 72);