Finite Group DatabasebetaFinite Group Databasebeta| order | 10449 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (C43⋊C9)⋊C27 |
| Sylow | C43 ⋊ C9⋊C27 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,43|a^3=d,b^3=c,d^3=e,b^a=bc,f^b=f^361233 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43⋊C3×C9⋊C27, C3×(C43⋊C9)⋊C27, #44533464, … |
| maximal normal subgroup of | C43⋊C3×C9⋊C27, C3×(C43⋊C9)⋊C27, #44533464, … |
| maximal quotient of | #44531934, #44531937, (C43⋊C9)⋊C81, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 116);