Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #13812⋊C3 |
| Fitting, Sylow | #13812 ⋊ C3 |
311 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 311 conjugacy classes of subgroups — too many to draw. Only its 34 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:
3,2^8|b^2=h,c^2=i,d^2=fg,e^2=gh,b^a=bcgh,c^a=efghi,e^a=cefi,h^a=fhi,i^a=gh,c^b=cf,d^b=dg,e^c=ef60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083598);