Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C4⋊C8×C251 ⋊ C2 |
| Sylow | C251 ⋊ #478 |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8032 |
Polycyclic presentation:
2^6,251|a^2=d,b^2=df,e^2=f,b^a=bd,c^a=ce,e^a=ef,g^a=g^250,e^c=ef,g^c=g^2502519 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #478×D251, C2×#30631988, #44560152, … |
| maximal normal subgroup of | #478×D251, C2×#30631988, #44560152, … |
| maximal quotient of | #44550376, #44550615, #44550629, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 850);