Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24 |
| direct product | Q8×3−1+2⋊Q8 |
| Sylow | 3−1+2 ⋊ Q82 |
671 conjugacy classes of subgroups.
| transitive degree | μt(G) = 576 |
155 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18790);