Finite Group DatabasebetaFinite Group Databasebeta| order | 2000 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | H(3,𝔽5) ⋊ M16 |
76 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^4,5^3|b^2=c,c^2=d,b^a=bd,f^a=f^4,g^a=g^4,e^b=e^2,g^b=g^2,e^c=e^4,g^c=g^4,f^e=fg38 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2000, 250);