Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4×C5 |
No aliases for this group.
| Fitting | C42×C52 ⋊ C2 |
| Sylow | C52 ⋊ #117 |
304 conjugacy classes of subgroups.
| transitive degree | μt(G) = 400 |
Polycyclic presentation:
2^5,5^2|b^2=e,c^2=d,c^a=ce,f^a=f^4,g^a=g^4212 conjugacy classes — view the full character table.
| maximal subgroup of | #13100241, #13100333, #13100435, … |
| maximal normal subgroup of | #13100241, #13100333, #13100435, … |
| maximal quotient of | #13102510, #13102514, #13102516, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 851);