Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
| direct product | C3×#13095314 |
| Fitting | C34×C19 ⋊ C3 |
| Sylow | C19 ⋊ C3×AΣL(1,𝔽27) |
252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
537 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28354776, C9×#13095314, #28354800, … |
| maximal normal subgroup of | #28354776, C9×#13095314, #28354800, … |
| maximal quotient of | C3×#17987309, C3×#17987311, C3×#17987312, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 245);