Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C25 ⋊ #331 |
126 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|a^2=c,c^2=f,d^2=ef,g^5=h,b^a=bd,d^a=de,g^a=g^2h,h^a=h^2,c^b=cf,d^b=def,g^c=g^4h^4,h^c=h^479 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 261);