Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C3×#2010 ⋊ C2 |
| Sylow | C3 ⋊ #23414 |
1980 conjugacy classes of subgroups.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^8,3|e^2=h,b^a=be,c^a=cf,e^a=eh,g^a=gh,c^b=cg,e^b=eh,f^b=fh,d^c=dh,i^d=i^272 conjugacy classes — view the full character table.
| maximal subgroup of | #72253883, #72253888, D3×#23414 |
| maximal normal subgroup of | #72253883, #72253888, D3×#23414 |
| maximal quotient of | #72271779 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 196588);