Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C3×#1779 ⋊ C2 |
| Sylow | C3 ⋊ #32878 |
6020 conjugacy classes of subgroups; only the 323 normal subgroups are shown.
This group has 6020 conjugacy classes of subgroups — too many to draw. Only its 323 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|e^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eh,i^a=i^2,e^b=eh,i^b=i^2114 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#32878, #72253290, #72253358 |
| maximal normal subgroup of | D3×#32878, #72253290, #72253358 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 318201);