Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C9 · Schur multiplier (H2) = C24×C3 |
| direct product | C2×C3×D4×C22⋊C9 |
| unambiguous semidirect product | C4⋊(C22×C3×C22⋊C9) |
| unambiguous semidirect product | (C23×C3×D4)⋊C9 |
| Sylow | C23×D4 ⋊ C3×C9 |
1794 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
360 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30905);