Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C16 · Schur multiplier (H2) = C22 |
| direct product | C3×(C2×D3)⋊(C3⋊C16) |
| unambiguous semidirect product | (C2×D3)⋊(C3×C3⋊C16) |
| Sylow | C33 ⋊ C22⋊C16 |
418 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 11466);