Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C1 |
| direct product | 3−1+2×#214 |
| unambiguous semidirect product | (C9×#214)⋊C3 |
| Sylow | C3×3−1+2 ⋊ SD16 |
248 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | #72219869, #72219901, 3−1+2×#932, … |
| maximal normal subgroup of | #72219901, 3−1+2×#932, #72219917 |
| maximal quotient of | #72219869 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1584);