Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C3×C4×C4⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #9674 |
736 conjugacy classes of subgroups.
| transitive degree | μt(G) = 384 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=dfg,c^2=e,d^2=g,f^2=h,b^a=bd,c^a=ce,d^b=dg,f^b=fg,i^b=i^2156 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 68523);