Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #107×C251 ⋊ C2 |
| Sylow | C251 ⋊ #440 |
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 49 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|a^2=e,c^2=e,d^2=f,b^a=bd,c^a=cf,d^a=df,d^b=df,g^b=g^250,g^c=g^2501772 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #440×D251, C2×#30631786, #44559160, … |
| maximal normal subgroup of | #440×D251, C2×#30631786, #44559160, … |
| maximal quotient of | #44549176, #44549221, #44549242, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 648);