Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of ((C3⋊D3)⋊C9)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×((C3⋊D3)⋊C9)⋊C2 |
| Fitting | C4×C32⋊C9 ⋊ C22 |
| derived, Sylow | C32⋊C9 ⋊ C22×C4 |
345 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 345 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 810);