Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×D4×C16 ⋊ C2 |
| Sylow | C3 ⋊ #33486 |
662 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=f,f^2=g,g^2=h,b^a=be,d^a=de,c^b=ce,i^d=i^2216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323149);