Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4294⋊Dic25 |
| derived, Hall | C19×C25 ⋊ C4×C9 |
| Hall | C25×#4294 ⋊ C4 |
| Hall | Dic475 ⋊ C9 |
| Hall | #4294 ⋊ Dic25 |
| Sylow | C25 ⋊ #4294⋊C4 |
| Sylow | C19 ⋊ C9×Dic25 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17100 |
Polycyclic presentation:
2,3,5,19,2,3,5|a^2=e,b^3=f,c^5=g^4,c^a=c^4g,d^a=d^18,g^a=g^4,d^b=d^7702 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 4);