Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4⋊C8×C251 ⋊ C2 |
| Sylow | C251 ⋊ #461 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8032 |
Polycyclic presentation:
2^6,251|a^2=f,b^2=d,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 | #44549545, #44549547, #44549566, … |
| maximal normal subgroup of | #44549545, #44549547, #44549566, … |
| maximal quotient of | #44549741, #44549755, #44549765, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 755);