Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C25 ⋊ #362 |
81 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 800 |
Polycyclic presentation:
2^6,5^2|a^2=c,b^2=f,c^2=f,d^2=e,e^2=f,g^5=h,b^a=bd,d^a=de,e^a=ef,g^a=g^2h,h^a=h^2,c^b=cf,d^b=def,e^b=ef,g^c=g^4h^4,h^c=h^458 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 247);