Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | Dic6×D27 |
| unambiguous semidirect product | (C3×D27)⋊Q8 |
| Sylow | C3×C27 ⋊ C2×Q8 |
170 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 170 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) = 432 |
135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 814);