Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | M16×3−1+2⋊C4 |
| unambiguous semidirect product | (M16×Dic9)⋊C3 |
| Sylow | 3−1+2 ⋊ C4×M16 |
460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C4×M16×AGL(1,ℤ/9), #72244777, #72252833 |
| maximal normal subgroup of | C4×M16×AGL(1,ℤ/9), #72244777, #72252833 |
| maximal quotient of | #72252901 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 9287);