Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C125 ⋊ SD16 |
40 conjugacy classes of subgroups.
| minimal degree | μ(G) = 133 |
| transitive degree | μt(G) = 1000 |
Polycyclic presentation:
2^4,5^3|a^2=d,c^2=d,e^5=f,f^5=g,b^a=bc,c^a=cd,e^a=e^4f^4g^4,f^a=f^4g^4,g^a=g^4,c^b=cd317 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 15);