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 ⋊ #6894 |
| 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 | #6894 |
| LCS | G ▷ C32×C43 ▷ C43 | |
| UCS | C1 ◁ C32 ◁ C9⋊C9 | |
124 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
3^5,43|a^3=e,b^3=d,b^a=bd,c^a=ce,f^b=f^36,f^c=f^6513 conjugacy classes — view the full character table.
| maximal subgroup of | C43⋊C3×#6894, C3×#23782814, #44534724, … |
| maximal normal subgroup of | C43⋊C3×#6894, C3×#23782814, #44534724, … |
| maximal quotient of | #44532249, #44532274, #44532277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10449, 198);