Finite Group DatabasebetaFinite Group Databasebeta| order | 10449 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | C43×C9⋊C9 ⋊ C3 |
| Sylow | C43 ⋊ #6897 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C43⋊C3 |
| commutator, socle, cosocle | C32×C43 | C33 |
| Fitting | C43×C9⋊C9 | C3 |
| prime radical | C32×C43⋊C3 | C32 |
| hypercenter | C9⋊C9 | C43⋊C3 |
| hypocenter | C43 | #6897 |
| LCS | G ▷ C32×C43 ▷ C43 | |
| UCS | C1 ◁ C32 ◁ C9⋊C9 | |
100 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 44 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,b^a=bd,c^a=ce,f^a=f^6,f^c=f^36513 conjugacy classes — view the full character table.
| maximal subgroup of | C43⋊C3×#6897, C3×#23782832, #44534756, … |
| maximal normal subgroup of | C43⋊C3×#6897, C3×#23782832, #44534756, … |
| maximal quotient of | #44532258, #44532283, #44532284, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 216);