Finite Group DatabasebetaFinite Group Databasebeta| order | 1539 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C32 |
No aliases for this group.
| Fitting | C3×C9×C19 ⋊ C3 |
| Sylow | C19 ⋊ #732 |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 513 |
Polycyclic presentation:
3^4,19|b^3=d^2,b^a=bc,c^a=cd,e^a=e^7179 conjugacy classes — view the full character table.
| maximal subgroup of | #17987369, #17987370, #17987371, … |
| maximal normal subgroup of | #17987369, #17987370, #17987371, … |
| maximal quotient of | #17987310, #17987319, #17987323, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1539, 35);