Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C82 · Schur multiplier (H2) = C43 |
No aliases for this group.
| Sylow | C3 ⋊ #8131 |
574 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 291 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 768 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=d,e^2=g,f^2=h,b^a=bd,i^c=i^2240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 59990);