Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#2916 ⋊ C2 |
| Sylow | C3 ⋊ #33659 |
546 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 167 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|c^2=eg,d^2=h,f^2=gh,g^2=h,b^a=be,c^a=cf,f^a=fg,g^a=gh,i^a=i^2,d^b=dh,f^b=fh,e^c=eh,f^c=fgh,g^c=gh84 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#33659, #72270492, #72270498, … |
| maximal normal subgroup of | D3×#33659, #72270492, #72270498, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 324483);