Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C3×C19×3−1+2 ⋊ C3 |
| Sylow | C19 ⋊ #6891 |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^5,19|a^3=d,b^a=bd,c^a=ce,f^c=f^7249 conjugacy classes — view the full character table.
| maximal subgroup of | #28353733, #28353734, #28353739, … |
| maximal normal subgroup of | #28353733, #28353734, #28353739, … |
| maximal quotient of | #28353504, #28353533, #28353551, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 179);