Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C33 |
No aliases for this group.
| Fitting | C2×C33×M16 ⋊ C2 |
| Sylow | C33 ⋊ #575 |
3668 conjugacy classes of subgroups; only the 835 normal subgroups are shown.
This group has 3668 conjugacy classes of subgroups — too many to draw. Only its 835 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|c^2=f,d^2=e,e^2=f,d^a=de,e^a=ef,g^a=g^2,h^a=h^2,i^a=i^2,d^b=df282 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 45936);