Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | Q8×((C22⋊C9)⋊C2)⋊C3 |
| unambiguous semidirect product | ((C22⋊C9)⋊C2)⋊(C3×Q8) |
582 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30474);