Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #62589⋊C3 |
| Fitting, Sylow | #62589 ⋊ C3 |
417 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 417 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 128 |
Polycyclic presentation:
3,2^8|b^2=i,d^2=gh,f^2=g,h^2=i,b^a=bce,c^a=e,e^a=cefg,c^b=cg,d^b=dh,f^b=fg,h^b=hi,d^c=di,e^c=eg,e^d=ei,f^d=fi59 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1084928);