Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2 |
| direct product | C5×C4⋊#168 |
| unambiguous semidirect product | C4⋊(C5×#168) |
| Sylow | C52 ⋊ C4⋊C8 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13099250, #13099252, #13099253, … |
| maximal normal subgroup of | #13099250, #13099252, #13099253, … |
| maximal quotient of | C5×#64677, C5×#64678, C5×C4⋊#672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 289);