Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C3 ⋊ #12833 |
358 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=f,b^2=d,d^2=g,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,g^a=gh,i^a=i^2,f^b=fh,e^c=eh,f^c=fh114 conjugacy classes — view the full character table.
| maximal subgroup of | #72228276 |
| maximal normal subgroup of | #72228276 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 85729);