Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
No aliases for this group.
| Fitting | C22×C3×#99 ⋊ C2 |
| Sylow | C3 ⋊ #20609 |
4122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|a^2=g,b^a=be,c^a=cf,d^a=dh,e^a=eh,f^b=fh,g^b=gh,e^c=eh,i^c=i^2102 conjugacy classes — view the full character table.
| maximal subgroup of | #72248130, D3×#20609, #72248381, … |
| maximal normal subgroup of | #72248130, D3×#20609, #72248381, … |
| maximal quotient of | #72248663, #72248668, #72271275, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 168834);