Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C2×C3×#410 ⋊ C2 |
| Sylow | C3 ⋊ #60070 |
4892 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,e^2=h,b^a=bf,f^a=fh,g^b=gh,d^c=dh,i^d=i^2126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033044);