Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C3×#1772 ⋊ C2 |
| Sylow | C3 ⋊ #13261 |
566 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=dfg,c^2=eh,d^2=gh,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,e^a=eh,i^a=i^2,d^b=dg,f^b=fg,g^b=gh102 conjugacy classes — view the full character table.
| maximal subgroup of | #72226026, #72226060, #72226196, … |
| maximal normal subgroup of | #72226026, #72226060, #72226196, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 88078);