Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C3 ⋊ #27694 |
626 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=eg,b^2=e,d^2=e,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=de,e^a=eh,f^a=fh,g^a=gh,c^b=cg,f^b=fh,i^b=i^2,d^c=dh,f^c=fh,i^d=i^272 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#27694, #72270640 |
| maximal normal subgroup of | D3×#27694, #72270640 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 251762);