Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C52 ⋊ C8 |
| Sylow | C52 ⋊ #324 |
216 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=f,c^2=e,b^a=bd,d^a=df,g^a=h,h^a=g^2,c^b=cf,g^c=g^2,h^c=h^2,g^e=g^4,h^e=h^446 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5758);