Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| direct product | C3×D3×Q8⋊C9 |
| unambiguous semidirect product | C3⋊(C2×C3×Q8⋊C9) |
| unambiguous semidirect product | (C3×D3×Q8)⋊C9 |
| derived | C3×Q8 ⋊ C2×C3×C9 |
241 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 241 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2164);