Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #101×C251 ⋊ C2 |
| Sylow | C251 ⋊ #413 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4016 |
Polycyclic presentation:
2^6,251|a^2=e,c^2=f,e^2=f,b^a=bd,d^a=df,e^b=ef,g^b=g^250,g^c=g^2501397 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44552047, #44552049, #44552055, … |
| maximal normal subgroup of | #44552047, #44552049, #44552055, … |
| maximal quotient of | #44548678, #44548682, #44548698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 532);