Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C16×C25 ⋊ C4 |
| Sylow | C25 ⋊ #346 |
81 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=d,d^2=e,e^2=f,g^5=h,b^a=bf,g^a=g^2h,h^a=h^2,g^c=g^4h^4,h^c=h^4136 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 182);