Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×#578⋊C9 |
| unambiguous semidirect product | (C3×#578)⋊C9 |
| Sylow | #578 ⋊ C3×C9 |
400 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18301);