Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C5×C22⋊#168 |
| unambiguous semidirect product | C22⋊(C5×#168) |
| Sylow | C52 ⋊ C22⋊C8 |
154 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13099315, #13099316, #13099317, … |
| maximal normal subgroup of | #13099315, #13099316, #13099317, … |
| maximal quotient of | C5×#64744, C5×#64745, C5×#64748, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 315);