Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C1 |
| direct product | Q8×Q8⋊C27 |
| Sylow | Q82 ⋊ C27 |
181 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1728 |
315 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2249);