Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#88724 |
| Fitting | C4×Q8×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C4×#41 |
965 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), #72269007 |
| maximal normal subgroup of | C4×#41×AGL(1,ℤ/9), #72269007 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18797);