Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C22⋊Q8×AGL(1,ℤ/9) |
| unambiguous semidirect product | D9⋊(C3×C22⋊Q8) |
| unambiguous semidirect product | (D9×C22⋊Q8)⋊C3 |
| Fitting | 3−1+2×C22⋊Q8 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C2×C22⋊Q8 |
1003 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,ℤ/9)×#525, AGL(1,ℤ/9)×#546 |
| maximal normal subgroup of | AGL(1,ℤ/9)×#525, AGL(1,ℤ/9)×#546 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19040);