Finite Group DatabasebetaFinite Group Databasebeta| order | 16064 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q8×C251 ⋊ C2 |
| Sylow | C251 ⋊ #520 |
294 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8032 |
Polycyclic presentation:
2^6,251|a^2=f,d^2=e,b^a=be,d^a=de,c^b=ce,g^b=g^250,g^c=g^250,g^d=g^2502534 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #44559192, #44559196, #44559203, … |
| maximal normal subgroup of | #44559192, #44559196, #44559203, … |
| maximal quotient of | #44552719, #44552725, #44552730, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16064, 1031);