Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C25×C3 |
| unambiguous semidirect product | #10592655⋊C3 |
| Fitting | C2×C22⋊C4×H(3,𝔽3) ⋊ C2 |
| Sylow | H(3,𝔽3) ⋊ #386 |
1133 conjugacy classes of subgroups.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^3,3,2^3,3^2|c^2=e,b^a=bg,h^a=h^2,i^a=i^2,c^b=cf,h^d=hi164 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 8569);