Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5 · Schur multiplier (H2) = C5 |
| unambiguous semidirect product | #87812⋊C5 |
| Sylow | H(3,𝔽5) ⋊ Q16 |
87 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^2,5,2^2,5^2|a^2=e,b^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^4,g^a=g^4,d^b=de,f^c=fg95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 170);