Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C19 ⋊ C9⋊C27 |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4617 |
Polycyclic presentation:
3^5,19|a^3=d,b^3=c,d^3=e,b^a=bc,f^b=f^7585 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×C9⋊C27, C3×#17987355, #28354723, … |
| maximal normal subgroup of | C19⋊C3×C9⋊C27, C3×#17987355, #28354723, … |
| maximal quotient of | #28353193, #28353196, #28353456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 116);