Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of #3714 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C1 |
| direct product | C9×#3719 |
| Sylow | C32×C9 ⋊ Q16 |
178 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1270);