Finite Group DatabasebetaFinite Group Databasebeta| order | 10449 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C43 ⋊ #6872 |
52 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,43|a^3=d,d^3=e,b^a=bc,c^a=ce,f^a=f^36,c^b=ce513 conjugacy classes — view the full character table.
| maximal subgroup of | C43⋊C3×#6872, C3×#23782727, #44533446, … |
| maximal normal subgroup of | C43⋊C3×#6872, C3×#23782727, #44533446, … |
| maximal quotient of | H(3,𝔽3)⋊(C43⋊C27), 3−1+2⋊(C43⋊C27), #44531911, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 111);