Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C3×#1765 ⋊ C2 |
| Sylow | C3 ⋊ C4×#444 |
1022 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=g,c^2=g,d^2=f,e^2=h,f^2=h,b^a=be,d^a=dh,e^a=eh,e^b=eh,i^c=i^2132 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168138);