Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C32 |
| direct product | C2×(C3×SL(2,𝔽3))⋊C9 |
| unambiguous semidirect product | (C2×C3×SL(2,𝔽3))⋊C9 |
| Fitting | C2×C3×Q8×C9 ⋊ C3 |
| Sylow | C2×Q8 ⋊ C32⋊C9 |
201 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 201 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) = 432 |
186 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 973);