Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×Q8×AGL(1,ℤ/9) |
| unambiguous semidirect product | D9⋊(C3×C4×Q8) |
| Fitting | C4×Q8×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C2×C4×Q8 |
929 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#41×AGL(1,ℤ/9), AGL(1,ℤ/9)×#550 |
| maximal normal subgroup of | C4×#41×AGL(1,ℤ/9), AGL(1,ℤ/9)×#550 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18795);