Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C2×C52×C16 ⋊ C2 |
| Sylow | C52 ⋊ #504 |
336 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|c^2=d,d^2=e,e^2=f,b^a=bf,g^a=g^4,h^a=h^4424 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 5116);