Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of #127⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3×C4 |
| direct product | C2×C9×#127⋊C3 |
| Fitting | C2×C9×#127 ⋊ C3 |
| derived | C42 ⋊ C22×C3×C9 |
| Sylow | C2×#127 ⋊ C3×C9 |
384 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18184);