Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| isoclinism | isoclinic class of A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C19×C25 · Schur multiplier (H2) = C2 |
| direct product | C19×C25×C22⋊C9 |
| unambiguous semidirect product | C22⋊(C9×C19×C25) |
| unambiguous semidirect product | (C22×C25)⋊(C9×C19) |
| derived, Sylow | C22 ⋊ C9×C19×C25 |
| Hall | C22×C19×C25 ⋊ C9 |
| Hall | C22×C25 ⋊ C9×C19 |
| Hall | C22×C19 ⋊ C9×C25 |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8550 |
5700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 32);