Finite Group DatabasebetaFinite Group Databasebeta| order | 10449 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C33 |
No aliases for this group.
| Fitting | C3×3−1+2×C43 ⋊ C3 |
| Sylow | C43 ⋊ C9⋊H(3,𝔽3) |
166 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
3^5,43|b^3=d,b^a=bd,c^a=ce,f^c=f^36513 conjugacy classes — view the full character table.
| maximal subgroup of | C43⋊C3×C9⋊H(3,𝔽3), C3×#23782799, #44534700, … |
| maximal normal subgroup of | C43⋊C3×C9⋊H(3,𝔽3), C3×#23782799, #44534700, … |
| maximal quotient of | #44532247, #44532270, #44532274, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 183);