Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C42 |
No aliases for this group.
| Sylow | C3 ⋊ #12581 |
854 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=e,b^2=f,c^2=h,d^2=h,b^a=bd,d^a=dg,f^a=fh,g^a=gh,i^a=i^2,e^b=egh,e^d=eh108 conjugacy classes — view the full character table.
| maximal subgroup of | #72247980, D3×#12581, #72247993, … |
| maximal normal subgroup of | #72247980, D3×#12581, #72247993, … |
| maximal quotient of | #72270415 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 84538);