Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #625 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×(C2×D3)⋊Dic3 |
| unambiguous semidirect product | (C2×D3)⋊(C9×Dic3) |
| Sylow | C32×C9 ⋊ C22⋊C4 |
344 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
270 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1326);