Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #10624725⋊C2 |
| Fitting, Sylow | #10624725 ⋊ C2 |
111 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 111 conjugacy classes of subgroups — too many to draw. Only its 34 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 81 |
Polycyclic presentation:
2,3^6|b^3=f,d^3=f,f^3=g,b^a=b^2d^2f^2,e^a=e^2g^2,c^b=ce,e^b=eg,d^c=dg102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1096);