Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C5×C25 ⋊ M16 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^4,5^3|b^2=c,c^2=d,e^5=g,b^a=bd,f^a=f^4,e^b=e^2g,g^b=g^2,e^c=e^4g^4,g^c=g^474 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 247);