Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C2×C5×#688 |
| Fitting | C2×C52×Q8 ⋊ C2 |
| Sylow | C52 ⋊ C2×SD16 |
174 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×#688, #13101731, #13101734, … |
| maximal normal subgroup of | Dic5×#688, #13101731, #13101734, … |
| maximal quotient of | C2×C5×#3940, C2×C5×#3941, C5×#65257, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 834);