Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22×C8×C251 ⋊ C2 |
| Sylow | C251 ⋊ #416 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8032 |
Polycyclic presentation:
2^6,251|a^2=e,c^2=f,d^2=f,b^a=bd,d^a=df,g^a=g^250,d^b=df,g^b=g^2504028 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44550201, #44550202, #44550208, … |
| maximal normal subgroup of | #44550201, #44550202, #44550208, … |
| maximal quotient of | #44548748, #44548774, #44548800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 546);