Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C3×#10591522 |
| Fitting | C2×C33×D4 ⋊ C22 |
| Sylow | C33 ⋊ #453 |
970 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 970 conjugacy classes of subgroups — too many to draw. Only its 116 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | #72220042, C3×#11864777, D3×#10591522, … |
| maximal normal subgroup of | C3×#11864777, D3×#10591522, #72220386, … |
| maximal quotient of | #72220042, C2×C3×#10591522 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 24612);