Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C32×D3×AGL(1,ℤ/8) |
| Fitting | C33×AGL(1,ℤ/8) ⋊ C2 |
| Sylow | C33 ⋊ C2×AGL(1,ℤ/8) |
2060 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C3⋊D3×AGL(1,ℤ/8) |
| maximal normal subgroup of | D3×C3⋊D3×AGL(1,ℤ/8) |
| maximal quotient of | C32×D3×#442 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45212);