Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C3 ⋊ #21776 |
1520 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|a^2=g,b^a=be,c^a=cf,d^a=de,e^a=eh,i^a=i^2,c^b=ce,f^b=fh,g^b=gh,g^d=gh90 conjugacy classes — view the full character table.
| maximal subgroup of | #72230732, #72231044, D3×#21776, … |
| maximal normal subgroup of | #72230732, #72231044, D3×#21776, … |
| maximal quotient of | #72270045, #72271425 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 178720);