Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C3×#1331 ⋊ C2 |
| Sylow | C3 ⋊ #11645 |
358 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 91 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|a^2=e,d^2=fh,e^2=g,f^2=h,b^a=bd,d^a=df,f^a=fh,c^b=cg,d^b=df,f^b=fh,i^c=i^2102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 79541);