Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #4268⋊C9 |
| Hall | C3×C7⋊C9 ⋊ D4 |
| Sylow | C7 ⋊ C9×#67 |
116 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 252 |
Polycyclic presentation:
2^2,3,2,3^2,7|c^3=e,b^a=bd,f^a=f^2,g^a=g^6,g^c=g^2117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 218);