Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C8×C251 ⋊ C2 |
| Sylow | C251 ⋊ #449 |
162 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 43 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 8032 |
Polycyclic presentation:
2^6,251|c^2=f,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^250,d^b=df,g^b=g^2502519 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #449×D251, C2×#30631834, #44559586, … |
| maximal normal subgroup of | #449×D251, C2×#30631834, #44559586, … |
| maximal quotient of | #44549296, #44549313, #44549364, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 696);