Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C19×C9⋊C9 ⋊ C3 |
| Sylow | C19 ⋊ C9×3−1+2 |
148 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|a^3=e,b^3=d,c^3=e,b^a=bd,f^c=f^7297 conjugacy classes — view the full character table.
| maximal subgroup of | C9×3−1+2×C19⋊C3, C3×#17987409, #28355918, … |
| maximal normal subgroup of | C9×3−1+2×C19⋊C3, C3×#17987409, #28355918, … |
| maximal quotient of | #28353495, #28353499, C9⋊C9×#4294, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 170);