Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M32×C251 ⋊ C2 |
| Sylow | C251 ⋊ #350 |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8032 |
Polycyclic presentation:
2^6,251|a^2=d,c^2=f,d^2=e,e^2=f,b^a=bc,g^a=g^250,c^b=cf,d^b=df,g^b=g^2502528 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #350×D251, C2×#30631472, #44551991, … |
| maximal normal subgroup of | #350×D251, C2×#30631472, #44551991, … |
| maximal quotient of | #44548290, #44548306, #44548319, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 334);