Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C3×#3021 ⋊ C2 |
| Sylow | C3 ⋊ #23882 |
1866 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,g^a=gh,c^b=cg,e^b=eh,i^b=i^2,e^c=eh,f^c=fh,e^d=eh,f^d=fh,i^d=i^269 conjugacy classes — view the full character table.
| maximal subgroup of | #72214518, D3×#23882, #72245918, … |
| maximal normal subgroup of | D3×#23882, #72245918, #72246050, … |
| maximal quotient of | #72214518, C2×#10826596, #72248041, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 200977);