Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#4093 |
| Fitting | C2×C52×Q8 ⋊ C2 |
| Sylow | C52 ⋊ #124 |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13099352, C5×#64697, C5×#64927, … |
| maximal normal subgroup of | #13099352, C5×#64697, C5×#64927, … |
| maximal quotient of | C5×#65266, C5×#65275, C5×#65277, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 840);