Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #20360⋊C3 |
| Fitting, Sylow | #20360 ⋊ C3 |
471 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 471 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 64 |
| transitive degree | μt(G) = 64 |
Polycyclic presentation:
3,2^8|b^2=g,c^2=h,h^2=i,c^a=cdegi,d^a=dehi,e^a=dg,c^b=cf,f^b=fi,g^c=gi,e^d=ei86 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1083821);