Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×C9⋊#1042 |
| unambiguous semidirect product | C9⋊(C17×#1042) |
| Fitting, Hall | C52×C9×C17 ⋊ C4 |
| derived, Hall | C52×C9 ⋊ C4×C17 |
| Hall | C52×C17 ⋊ Dic9 |
| Hall | C9×C17 ⋊ #1042 |
| Sylow | C52 ⋊ C17×Dic9 |
| Sylow | C9 ⋊ C17×#1042 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3060 |
1581 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 194);