Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C27 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #568⋊C27 |
| Sylow | #568 ⋊ C27 |
183 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 183 conjugacy classes of subgroups — too many to draw. Only its 59 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:
2^2,3,2,3^2,2^3|b^2=d,c^3=e,d^2=i,e^3=f,g^2=i,h^2=i,b^a=bi,g^c=gh,h^c=g,h^g=hi342 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 2255);