Finite Group DatabasebetaFinite Group Databasebeta| order | 10449 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C43×C81 ⋊ C3 |
| Sylow | C43 ⋊ C81⋊C3 |
32 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,43|a^3=c,c^3=d,d^3=e,b^a=be,f^b=f^361233 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43⋊C3×C81⋊C3, C3×#23782742, #44534464, … |
| maximal normal subgroup of | C43⋊C3×C81⋊C3, C3×#23782742, #44534464, … |
| maximal quotient of | #44532086, (C3×C43⋊C3)⋊C81, (C43⋊C9)⋊C81, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 126);