Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C25 ⋊ #356 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|a^2=d,b^2=f,c^2=f,d^2=f,g^5=h,b^a=bc,c^a=ce,e^a=ef,g^a=g^4h^4,h^a=h^4,c^b=cf,d^b=def,d^c=df181 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 106);