Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #137×C251 ⋊ C2 |
| Sylow | C251 ⋊ #575 |
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 4016 |
Polycyclic presentation:
2^6,251|d^2=f,e^2=f,b^a=be,c^a=cf,e^a=ef,e^b=ef,g^b=g^250,g^d=g^2501397 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44559715, #44559717, #44559723, … |
| maximal normal subgroup of | #44559715, #44559717, #44559723, … |
| maximal quotient of | #44558881, #44558883, #44558952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 1348);