Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C3×#1779 ⋊ C2 |
| Sylow | C3 ⋊ #23918 |
2596 conjugacy classes of subgroups; only the 263 normal subgroups are shown.
This group has 2596 conjugacy classes of subgroups — too many to draw. Only its 263 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^2,c^b=cg,f^c=fh,i^c=i^2108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 201310);