Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C25×#101 ⋊ C2 |
| Sylow | C25 ⋊ #355 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^6,5^2|b^2=c,c^2=f,d^2=f,g^5=h,b^a=bd,c^a=ce,d^a=df,g^a=g^4h^4,h^a=h^4,d^b=def,e^b=ef,d^c=df145 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 36);