Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C3×C22⋊#95 ⋊ C2 |
| Sylow | C3 ⋊ C4×#386 |
3366 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=h,d^2=g,b^a=be,c^a=cf,i^d=i^2168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 90712);