Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C3 |
No aliases for this group.
| Fitting | C3×C9×C4⋊Q8 ⋊ C2 |
| Sylow | C3×C9 ⋊ D4×Q8 |
1400 conjugacy classes of subgroups.
| transitive degree | μt(G) = 864 |
Polycyclic presentation:
2^6,3^3|a^2=f,b^2=f,c^2=f,d^2=f,h^3=i,b^a=bf,g^a=g^2,h^a=h^2i^2,i^a=i^2,c^b=cf,d^b=df,d^c=de207 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 20338);