Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C25×#127 ⋊ C2 |
| Sylow | C25 ⋊ #493 |
243 conjugacy classes of subgroups.
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|a^2=e,e^2=f,g^5=h,b^a=be,c^a=ce,g^a=g^4h^4,h^a=h^4,c^b=cd,e^b=ef,e^c=ef190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 697);