Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C52×C22⋊C4 ⋊ C2 |
| Sylow | C52 ⋊ #99 |
208 conjugacy classes of subgroups.
| transitive degree | μt(G) = 200 |
Polycyclic presentation:
2^5,5^2|b^2=c,b^a=bd,c^a=ce,f^a=f^4,g^a=g^4,d^b=de131 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3938, #13100586, #13100588, … |
| maximal normal subgroup of | D5×#3938, #13100586, #13100588, … |
| maximal quotient of | #13099485, #13099486, #13099501, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 332);