Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C19×AΣL(1,𝔽27) ⋊ C3 |
| Sylow | C19 ⋊ #6913 |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^5,19|c^3=e,b^a=bd,d^a=de,c^b=ce,f^c=f^7137 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×#6913, C3×#17987520, #28356589, … |
| maximal normal subgroup of | C19⋊C3×#6913, C3×#17987520, #28356589, … |
| maximal quotient of | #28353762, #28353765, #28353770, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 281);