Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×C8×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #20557 |
1030 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,c^2=f,f^2=h,b^a=be,d^a=de,i^a=i^2,c^b=ceh,i^b=i^2,i^d=i^2180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168481);