Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C22×C3×C4⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #9133 |
784 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=dfgh,d^2=gh,f^2=h,b^a=bd,c^a=ce,d^a=dg,i^a=i^2,d^b=dh,f^b=fh138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 65233);