Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C27 · Schur multiplier (H2) = C23 |
| direct product | D3×D4×C27 |
| Fitting | C3×D4×C27 ⋊ C2 |
| Sylow | C3×C27 ⋊ C2×D4 |
240 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
405 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1063);