Finite Group DatabasebetaFinite Group Databasebeta| order | 768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×#2121 ⋊ C2 |
| Sylow | C3 ⋊ #12767 |
878 conjugacy classes of subgroups.
| transitive degree | μt(G) = 48 |
Polycyclic presentation:
2^8,3|a^2=f,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,e^b=egh,f^b=fg,d^c=dg,f^c=fh,i^c=i^2,e^d=eh,f^d=fh57 conjugacy classes — view the full character table.
| maximal subgroup of | #72271276, #72271279, #72271280, … |
| maximal normal subgroup of | #72271276, #72271279, #72271280, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(768, 85410);