Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4090 |
| Sylow | C52 ⋊ C4⋊Q8 |
174 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13099354, C5×#64698, C5×#64929, … |
| maximal normal subgroup of | #13099354, C5×#64698, C5×#64929, … |
| maximal quotient of | C5×#65263, C5×#65265, C5×#65261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 837);