Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽5) ⋊ SD16 |
66 conjugacy classes of subgroups.
| minimal degree | μ(G) = 58 |
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^4,5^3|a^2=c,c^2=d,b^a=bcd,e^a=e^2,f^a=f^3g^3,c^b=cd,e^b=f^4g,f^b=e^4g^4,g^b=g^4,e^c=e^4,f^c=f^4g^2,f^e=fg41 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 268);