Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C3×C4×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #9148 |
800 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=dfh,c^2=g,d^2=gh,f^2=gh,b^a=bd,c^a=ce,d^a=dg,i^a=i^2,d^b=dh,f^b=fh138 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 65308);