Finite Group DatabasebetaFinite Group Databasebeta| order | 10449 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C9 |
No aliases for this group.
| Fitting | C92×C43 ⋊ C3 |
| Sylow | C43 ⋊ #6898 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C32 | C32×C43⋊C3 |
| commutator, socle, cosocle | C32×C43 | C33 |
| Fitting | C92×C43 | C3 |
| prime radical | C32×C43⋊C3 | C32 |
| hypercenter | C92 | C43⋊C3 |
| hypocenter | C43 | #6898 |
| LCS | G ▷ C32×C43 ▷ C43 | |
| UCS | C1 ◁ C32 ◁ C92 | |
100 conjugacy classes of subgroups.
Polycyclic presentation:
3^5,43|b^3=e,c^3=d^2,b^a=bd,c^a=ce,f^a=f^361185 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C43⋊C3×#6898, C3×#23782835, #44534757, … |
| maximal normal subgroup of | C43⋊C3×#6898, C3×#23782835, #44534757, … |
| maximal quotient of | #44532262, #44532286, #44532300, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 219);