Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×#1767 ⋊ C2 |
| Sylow | C3 ⋊ #8234 |
696 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=e,d^2=g,f^2=gh,b^a=bd,d^a=dg,f^a=fgh,i^a=i^2,c^b=ch,d^b=dh,i^b=i^2120 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 60537);