Finite Group DatabasebetaFinite Group Databasebeta| order | 15300 |
| isoclinism | isoclinic class of D17 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C52×C9 · Schur multiplier (H2) = C2×C5 |
| direct product | C2×C52×C9×D17 |
| unambiguous semidirect product | C17⋊(C22×C52×C9) |
| unambiguous semidirect product | (C2×C17)⋊(C2×C52×C9) |
| Fitting | C2×C52×C9×C17 ⋊ C2 |
| derived, Sylow | C17 ⋊ C22×C52×C9 |
| Hall | C52×C9×C17 ⋊ C22 |
| Hall | C52×C17 ⋊ C22×C9 |
| Hall | C9×C17 ⋊ C22×C52 |
240 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7650 |
4500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15300, 214);