Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C33 |
No aliases for this group.
| Fitting | C33×#135 ⋊ C2 |
| Sylow | C33 ⋊ #576 |
3752 conjugacy classes of subgroups; only the 619 normal subgroups are shown.
This group has 3752 conjugacy classes of subgroups — too many to draw. Only its 619 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^6,3^3|e^2=f,b^a=bf,g^a=g^2,h^a=h^2,i^a=i^2,c^b=cf,d^b=df,d^c=de,e^c=ef,e^d=ef204 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45957);