Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#3414 ⋊ C2 |
| Sylow | C3 ⋊ #33595 |
706 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|b^2=e,e^2=h,f^2=gh,g^2=h,b^a=be,c^a=cf,e^a=eh,f^a=fg,g^a=gh,i^a=i^2,d^b=dh,i^b=i^2,f^c=fg,g^c=gh72 conjugacy classes — view the full character table.
| maximal subgroup of | #72270144, #72270159, #72270164, … |
| maximal normal subgroup of | #72270144, #72270159, #72270164, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 323971);