Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×Dic6×C22⋊C9 |
| unambiguous semidirect product | (C2×C3)⋊(Q8×C22⋊C9) |
| unambiguous semidirect product | (C23×Dic6)⋊C9 |
810 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 144 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30666);