Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | D25×#4294⋊C2 |
| unambiguous semidirect product | (C25×#4294⋊C2)⋊C2 |
| unambiguous semidirect product | (D25×#4294)⋊C2 |
| unambiguous semidirect product | (C25⋊(#4294⋊C2))⋊C2 |
| derived, Hall | C19×C25 ⋊ C22×C9 |
| Hall | C25×#4294 ⋊ C22 |
| Hall | D19×D25 ⋊ C9 |
| Hall | #4294 ⋊ C2×D25 |
| Sylow | C25 ⋊ C2×#4294⋊C2 |
| Sylow | C19 ⋊ C2×C9×D25 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4275 |
378 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 16);