Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (D9⋊C9)⋊C9 |
| unambiguous semidirect product | #10624561⋊C2 |
| Fitting, Sylow | #10624561 ⋊ C2 |
170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 170 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=eg,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 | AGL(1,ℤ/9)×C9⋊C9, #72243185, #72243188, … |
| maximal normal subgroup of | AGL(1,ℤ/9)×C9⋊C9, #72243185, #72243188, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 731);