Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C42 |
No aliases for this group.
| Fitting | C2×C3×C4×M16 ⋊ C2 |
| Sylow | C3 ⋊ #21203 |
2246 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,b^2=egh,c^2=f,d^2=h,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^2,d^b=dh144 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 173255);