Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C3 ⋊ #33360 |
1188 conjugacy classes of subgroups; only the 311 normal subgroups are shown.
This group has 1188 conjugacy classes of subgroups — too many to draw. Only its 311 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:
2^8,3|a^2=f,c^2=h,d^2=h,e^2=h,b^a=be,e^a=eg,g^a=gh,i^a=i^2,e^b=eh,f^b=fgh,d^c=dh,f^e=fh90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322377);