Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C2×C3×#442 ⋊ C2 |
| Sylow | C3 ⋊ #60176 |
2818 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
Polycyclic presentation:
2^8,3|a^2=g,c^2=gh,f^2=h,b^a=bf,c^a=ch,f^a=fh,f^b=fh,e^d=eh,i^e=i^2126 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11659463, #72222679, D3×#60176, … |
| maximal normal subgroup of | C3×#11659463, D3×#60176, #72225859, … |
| maximal quotient of | C3×#11659463, #72222679 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 1033844);