Finite Group DatabasebetaFinite Group Databasebeta| order | 17100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4294⋊#1035 |
| derived, Hall | C19×C25 ⋊ C4×C9 |
| Hall | C25×#4294 ⋊ C4 |
| Hall | C19⋊#1035 ⋊ C9 |
| Hall | #4294 ⋊ #1035 |
| Sylow | C25 ⋊ #4294⋊C4 |
| Sylow | C19 ⋊ C9×#1035 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4275 |
Polycyclic presentation:
2,3,2,5,19,3,5|a^2=c,b^3=f,d^5=g,d^a=d^2g,e^a=e^18,g^a=g^2,e^b=e^11,d^c=d^4g^4,g^c=g^4216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17100, 15);