Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C19⋊#6862 |
| Sylow | C19 ⋊ #6862 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|a^3=e^2,b^3=d,b^a=bc,c^a=cd,c^b=ce,f^b=f^7233 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×#6862, C3×C19⋊#6862, #28353716, … |
| maximal normal subgroup of | C19⋊C3×#6862, C3×C19⋊#6862, #28353716, … |
| maximal quotient of | #28353161, #28353162, #28353163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 87);