Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C4⋊C16 ⋊ C2 |
| Sylow | C3 ⋊ #12811 |
510 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=d,e^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eg,g^a=gh,i^a=i^2,e^c=eg,g^c=gh,i^c=i^2138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 85610);