Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C3×#1493 ⋊ C2 |
| Sylow | C3 ⋊ #8357 |
710 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=f,c^2=h,d^2=h,f^2=gh,b^a=bd,c^a=ce,d^a=dg,i^a=i^2,d^b=dh,e^b=eg,f^b=fgh,i^b=i^2,d^c=dg,i^c=i^290 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 61140);