Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C32×C9×C19 ⋊ C3 |
| Sylow | C19 ⋊ H(3,𝔽3)⋊C9 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|a^3=d,b^a=bc,c^a=ce,f^a=f^7,c^b=ce,f^b=f^7537 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×H(3,𝔽3)⋊C9, C3×#17987344, #28354678, … |
| maximal normal subgroup of | C19⋊C3×H(3,𝔽3)⋊C9, C3×#17987344, #28354678, … |
| maximal quotient of | #28353154, #28353159, #28353161, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 105);