Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C33 ⋊ C22×SD16 |
1416 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 180 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=f,b^2=f,c^2=f,e^2=f,d^a=de,e^a=ef,h^a=h^2,d^b=de,e^b=ef,g^b=g^2,d^c=de,e^c=ef,i^c=i^2,e^d=ef96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 37606);