Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C25 ⋊ C2 |
| Sylow | C25 ⋊ #137 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|b^2=e,c^2=d,d^2=e,f^5=g,c^a=cd,d^a=de,f^a=f^4g^4,g^a=g^4,c^b=ce131 conjugacy classes — view the full character table.
| maximal subgroup of | #13098021, #13098023, #13098027, … |
| maximal normal subgroup of | #13098021, #13098023, #13098027, … |
| maximal quotient of | #13097978, #13097979, #13097980, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 130);