Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#63383⋊C3 |
| unambiguous semidirect product | (C2×#63383)⋊C3 |
| Fitting | C2×M16×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C2×#100 |
592 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
146 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#100×AGL(1,ℤ/9), C2×#10588879⋊C3, C2×#10588502⋊C3 |
| maximal normal subgroup of | C2×#100×AGL(1,ℤ/9), C2×#10588879⋊C3, C2×#10588502⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 9299);