Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C19×C81 ⋊ C3 |
| Sylow | C19 ⋊ C81⋊C3 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1539 |
Polycyclic presentation:
3^5,19|a^3=c,c^3=d,d^3=e,b^a=be,f^b=f^11585 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×C81⋊C3, C3×#17987366, #28355723, … |
| maximal normal subgroup of | C19⋊C3×C81⋊C3, C3×#17987366, #28355723, … |
| maximal quotient of | #28353346, #28353351, #28353456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 127);