Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C24 |
| direct product | C2×#67×C22⋊C9 |
| unambiguous semidirect product | (C23×#67)⋊C9 |
1338 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 1338 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) = 72 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C22⋊C9×(C22⋊C9)⋊C2, C2×#72220166, C2×#67×#1094 |
| maximal normal subgroup of | C2×#67×#1094 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30705);