Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25 |
| direct product | C2×#63497⋊C3 |
| unambiguous semidirect product | (C2×#63497)⋊C3 |
| Sylow | 3−1+2 ⋊ C2×#123 |
1144 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, 19685);