Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23×C3 |
| direct product | C2×#638⋊C9 |
| unambiguous semidirect product | (C2×#638)⋊C9 |
| Fitting | C23×C32⋊C9 ⋊ C2 |
| Sylow | C32⋊C9 ⋊ C2×D4 |
393 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 393 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
186 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1109);