Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | #106×C3⋊D9 |
| Fitting | C3×C9×#106 ⋊ C2 |
| Sylow | C3×C9 ⋊ C2×#106 |
650 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 175 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 864 |
210 conjugacy classes — view the full character table.
| maximal subgroup of | C3⋊D9×#442, #106×C9⋊D9, #106×C3⋊AGL(1,ℤ/9) |
| maximal normal subgroup of | C3⋊D9×#442, #106×C3⋊AGL(1,ℤ/9) |
| maximal quotient of | #106×C9⋊D9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 10159);