Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#11721074 |
| Sylow | H(3,𝔽3) ⋊ C2×#137 |
1059 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
98 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 16709);