Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#1395 ⋊ C2 |
| Sylow | C3 ⋊ #12634 |
452 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 109 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=e,b^2=f,c^2=e,d^2=h,e^2=h,b^a=bd,c^a=ch,d^a=dh,f^a=fgh,d^b=dg,g^b=gh,i^c=i^2,f^d=fh72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84766);