Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#2180 ⋊ C2 |
| Sylow | C3 ⋊ #33469 |
646 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,c^2=fg,e^2=g,g^2=h,b^a=be,c^a=cg,e^a=eg,g^a=gh,e^b=egh,f^b=fh,g^b=gh,d^c=dh,e^c=eh,i^d=i^269 conjugacy classes — view the full character table.
| maximal subgroup of | #72222750, #72222752, #72222780, … |
| maximal normal subgroup of | D3×#33469, #72258527, #72258533 |
| maximal quotient of | #72222750, #72222752, #72222780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323022);