Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C3 ⋊ #8020 |
1350 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=g,d^2=g,b^a=bd,d^a=dg,f^a=fgh,i^a=i^2,c^b=ch,d^b=dh144 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#8020, #72247861, #72255480, … |
| maximal normal subgroup of | D3×#8020, #72247861, #72255480, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 59588);