Finite Group DatabasebetaFinite Group Databasebeta| order | 10449 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | #11923957⋊C9 |
| Fitting | C43×C9⋊C9 ⋊ C3 |
| Sylow | C43 ⋊ C9×3−1+2 |
148 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,43|a^3=e,b^3=d,c^3=e,b^a=bd,f^c=f^6561 conjugacy classes — view the full character table.
| maximal subgroup of | C9×3−1+2×C43⋊C3, C3×#11923957⋊C9, #44534659, … |
| maximal normal subgroup of | C9×3−1+2×C43⋊C3, C3×#11923957⋊C9, #44534659, … |
| maximal quotient of | #44532236, #44532240, C9⋊C9×C43⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 171);