Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C22×C3 |
| direct product | C32×D3×Dic6 |
| unambiguous semidirect product | (C3×D3)⋊(C32×Q8) |
| Sylow | C34 ⋊ C2×Q8 |
800 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 800 conjugacy classes of subgroups — too many to draw. Only its 216 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
243 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 3322);