Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C53 |
No aliases for this group.
| Sylow | C53 ⋊ Q16 |
576 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2000 |
Polycyclic presentation:
2^4,5^3|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^4,f^a=f^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, 615);