Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×#10591232 |
| Sylow | C33 ⋊ #410 |
1002 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
234 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 24165);