Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C33 ⋊ #474 |
680 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 104 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=e,b^2=d,c^2=e,e^2=f,b^a=be,c^a=cd,i^a=i^2,c^b=cef,e^b=ef,g^b=g^2,h^c=h^2117 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 22342);