Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C33×C22⋊C4 ⋊ C22 |
| Sylow | C33 ⋊ C2×#123 |
1690 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^3|d^2=ef,g^a=g^2,h^a=h^2,c^b=cf,d^b=de,g^b=g^2,i^b=i^2,d^c=df126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 44350);