Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#63369⋊C3 |
| unambiguous semidirect product | (C2×#63369)⋊C3 |
| Fitting | C2×C4⋊C4×3−1+2 ⋊ C2 |
| Sylow | 3−1+2 ⋊ C2×#102 |
652 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 8700);