Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C22×C3 |
| direct product | C3×D4⋊#622 |
| unambiguous semidirect product | D4⋊(C3×#622) |
| Sylow | C33 ⋊ D4⋊C8 |
460 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 23201);