Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×C3×#362 ⋊ C2 |
| Sylow | C3 ⋊ #13412 |
430 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 95 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|b^2=h,c^2=d,e^2=gh,f^2=g,g^2=h,b^a=bd,c^a=ce,e^a=eg,f^a=fg,g^a=gh,i^a=i^2,c^b=cf,e^b=eg,f^b=fgh,g^b=gh,e^c=eg,f^c=fgh,g^c=gh,i^c=i^272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 88942);