Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
288 conjugacy classes of subgroups; only the 29 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 29 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^6,3,2^2|a^2=f,b^2=c,c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^2,h^a=hi,d^b=def,e^b=ef,d^c=df,h^g=i,i^g=hi37 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1085998);