Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C25×C3 |
| unambiguous semidirect product | #10596237⋊C3 |
| Fitting | C2×Q16×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #578 |
928 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^4,3,2^2,3^2|c^2=g,d^2=g,f^2=g,b^a=bg,h^a=h^2,i^a=i^2,d^c=df,f^c=fg,f^d=fg,h^e=hi122 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 19529);