Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C3×#509 ⋊ C2 |
| Sylow | C3 ⋊ #62636 |
2078 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|f^2=gh,g^2=h,b^a=bf,e^a=eh,f^a=fg,g^a=gh,f^b=fg,g^b=gh,d^c=dh,i^d=i^290 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11701722, #72222759, #72222779, … |
| maximal normal subgroup of | C3×#11701722, #72228227, D3×#62636, … |
| maximal quotient of | C3×#11701722, #72222759, #72222779 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1076103);