Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | 3−1+2⋊#4294 |
| Sylow | C19 ⋊ 3−1+2⋊C9 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|a^3=d,b^3=e,b^a=bc,c^a=ce,f^a=f^7,c^b=ce249 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×3−1+2⋊C9, C3×3−1+2⋊#4294, #28354678, … |
| maximal normal subgroup of | C19⋊C3×3−1+2⋊C9, C3×3−1+2⋊#4294, #28354678, … |
| maximal quotient of | 3−1+2⋊#10587018, #28353162, #28353165, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 107);