Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C8×C16 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #7136 |
306 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 207 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=d,b^2=e,d^2=f,e^2=g,f^2=h,b^a=bc,i^a=i^2288 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 56396);