Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C2×C4 |
| direct product | C5×#4031 |
| Fitting | C52×C22⋊C4 ⋊ C2 |
| Sylow | C52 ⋊ #124 |
186 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#4031, #13105128, #13105130, … |
| maximal normal subgroup of | D5×#4031, #13105128, #13105130, … |
| maximal quotient of | C5×#64935, C5×#64939, C5×#64962, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 778);