Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×#4022 |
| Fitting | C42×C52 ⋊ C2 |
| Sylow | C52 ⋊ #126 |
150 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
230 conjugacy classes — view the full character table.
| maximal subgroup of | #13104983, #13104989, #13104992, … |
| maximal normal subgroup of | #13104983, #13104989, #13104992, … |
| maximal quotient of | C5×#64947, C5×#64965, C5×C5⋊#401, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 769);