Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C4×M32 ⋊ C2 |
| Sylow | C3 ⋊ #33463 |
652 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,c^2=f,e^2=gh,f^2=h,g^2=h,b^a=be,d^a=dh,e^a=eg,g^a=gh,i^a=i^2,e^b=eg,g^b=gh,i^b=i^2144 conjugacy classes — view the full character table.
| maximal subgroup of | #72225831, D3×#33463, #72226258 |
| maximal normal subgroup of | #72225831, D3×#33463, #72226258 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 322982);