Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | (C3×AGL(1,ℤ/9))⋊C9 |
| Fitting, Sylow | #10624560 ⋊ C2 |
230 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 162 |
Polycyclic presentation:
2,3^6|b^3=g,c^3=g,d^3=f,d^a=d^2f^2,f^a=f^2,c^b=ce,d^b=df126 conjugacy classes — view the full character table.
| maximal subgroup of | C9×#92265, #72243240, #72243245, … |
| maximal normal subgroup of | C9×#92265, #72243240, #72243245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 728);