Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4133 |
| Sylow | C52 ⋊ #131 |
130 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
125 conjugacy classes — view the full character table.
| maximal subgroup of | #13103755, #13103756, #13103757, … |
| maximal normal subgroup of | #13103755, #13103756, #13103757, … |
| maximal quotient of | C5×#65701, C5×#65702, C5×#65704, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1074);