Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4036 |
| Sylow | C52 ⋊ #125 |
138 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#64870, #13100154, #13100610, … |
| maximal normal subgroup of | C5×#64870, #13100154, #13100610, … |
| maximal quotient of | C5×#64950, C5×#64944, C5×#64943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 783);