Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D25×#4294 |
| unambiguous semidirect product | C25⋊(C22×#4294) |
| unambiguous semidirect product | (C2×C25)⋊(C2×#4294) |
| derived, Hall | C19×C25 ⋊ C22×C9 |
| Hall | C25×#4294 ⋊ C22 |
| Hall | C2×C19×D25 ⋊ C9 |
| Sylow | C25 ⋊ C22×#4294 |
| Sylow | C19 ⋊ C2×C9×D25 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8550 |
756 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 18);