Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
| direct product | D4×#6226 |
| Sylow | C3×C9 ⋊ D4×Q8 |
1400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
285 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19968);