Finite Group DatabasebetaFinite Group Databasebeta| order | 10449 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Sylow | C43 ⋊ #6899 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C43⋊C3 |
| commutator, socle, cosocle | C32×C43 | C33 |
| Fitting | C43×C32⋊C9 | C3 |
| prime radical | C33×C43 | C32 |
| hypercenter | C32⋊C9 | C43⋊C3 |
| hypocenter | C43 | #6899 |
| LCS | G ▷ C32×C43 ▷ C43 | |
| UCS | C1 ◁ C32 ◁ C32⋊C9 | |
110 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 47 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=de,c^3=d^2,b^a=bd,c^a=ce,f^c=f^36513 conjugacy classes — view the full character table.
| maximal subgroup of | C43⋊C3×#6899, C3×#23782837, #44534755, … |
| maximal normal subgroup of | C43⋊C3×#6899, C3×#23782837, #44534755, … |
| maximal quotient of | #44532263, #44532282, #44532287, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 221);