Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C3×C19×C27 ⋊ C3 |
| Sylow | C19 ⋊ C32⋊C27 |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|a^3=d,d^3=e,b^a=bc,f^b=f^7585 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×C32⋊C27, C3×#17987332, #28354617, … |
| maximal normal subgroup of | C19⋊C3×C32⋊C27, C3×#17987332, #28354617, … |
| maximal quotient of | #28353146, #28353148, #28353150, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 93);