Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×#10592851 |
| Sylow | C33 ⋊ #442 |
1096 conjugacy classes of subgroups; only the 290 normal subgroups are shown.
This group has 1096 conjugacy classes of subgroups — too many to draw. Only its 290 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
234 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C3⋊D3×#442, D3×#10592851, #72245396, … |
| maximal normal subgroup of | C3×C3⋊D3×#442, D3×#10592851, #72245396 |
| maximal quotient of | #72254737 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 29250);