Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×#4004 |
| Sylow | C52 ⋊ C4⋊C8 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13099770, #13099771, #13099772, … |
| maximal normal subgroup of | #13099770, #13099771, #13099772, … |
| maximal quotient of | C5×#64861, C5×#64883, C5×#64884, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 481);