Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C5 |
No aliases for this group.
| Fitting | C23×C52 ⋊ C4 |
| Sylow | C52 ⋊ #99 |
158 conjugacy classes of subgroups.
| transitive degree | μt(G) = 40 |
Polycyclic presentation:
2^5,5^2|a^2=c,b^a=bd,d^a=de,f^a=f^3,g^a=g^2,c^b=ce,f^c=f^4,g^c=g^459 conjugacy classes — view the full character table.
| maximal subgroup of | #13099940, #13099943, #13100012, … |
| maximal normal subgroup of | #13099940, #13099943, #13100012, … |
| maximal quotient of | #13100381, #13100384, #13100387, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 563);