Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C22 |
| direct product | C5×C22⋊#170 |
| unambiguous semidirect product | C22⋊(C5×#170) |
| Sylow | C52 ⋊ C22⋊C8 |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13099828, #13099829, #13099830, … |
| maximal normal subgroup of | #13099828, #13099829, #13099830, … |
| maximal quotient of | C5×#64913, C5×C22⋊#674, C5×#64912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 489);