Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C3 · Schur multiplier (H2) = C24×C3 |
| unambiguous semidirect product | #10596002⋊C3 |
| Fitting | H(3,𝔽3)×#117 ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #552 |
825 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^4,3,2^2,3^2|a^2=g,c^2=f,d^2=g,c^a=cg,h^a=h^2,i^a=i^2,d^b=df,h^e=hi155 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 18572);