Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C3 |
| direct product | C2×D4×C3⋊#157 |
| Fitting | C2×C33×D4 ⋊ C4 |
| Sylow | C33 ⋊ C2×C4×D4 |
1432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 47579);