Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4065 |
| Fitting | C52×Q16 ⋊ C2 |
| Sylow | C52 ⋊ #135 |
142 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#64907, C5×#64909, #13100191, … |
| maximal normal subgroup of | C5×#64907, C5×#64909, #13100191, … |
| maximal quotient of | C5×#65108, C5×#65085, C5×#65089, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 812);