Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C82 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C3 ⋊ #7330 |
110 conjugacy classes of subgroups.
| transitive degree | μt(G) = 768 |
Polycyclic presentation:
2^8,3|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,g^2=h,b^a=bg,d^a=dh,c^b=ch,i^b=i^2168 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#7330, #72244997, #72245006, … |
| maximal normal subgroup of | D3×#7330, #72244997, #72245006, … |
| maximal quotient of | #72245317, #72245364 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 56897);