Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C3 |
No aliases for this group.
| Fitting | C33×D8 ⋊ C4 |
| Sylow | C33 ⋊ #442 |
460 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 71 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^3|a^2=d,e^2=f,c^a=cf,g^a=g^2,h^a=hi,i^a=hi^2,c^b=ce,e^b=ef,e^c=ef,h^d=h^2,i^d=i^278 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 39438);