Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | (C19⋊C3)⋊(C27⋊C3) |
| Sylow | C19 ⋊ C3×C27⋊C3 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^5,19|a^3=d,d^3=e,b^a=be,f^a=f^4,f^c=f^11,f^d=f^7153 conjugacy classes — view the full character table.
| maximal subgroup of | #28356718, #28356719, #28356720, … |
| maximal normal subgroup of | #28356718, #28356719, #28356720, … |
| maximal quotient of | #28356875, C9×#13095342, C9×#13095343, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 356);