Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#4040 |
| Fitting | C52×C4⋊C4 ⋊ C2 |
| Sylow | C52 ⋊ #123 |
182 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 182 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) = 160 |
170 conjugacy classes — view the full character table.
| maximal subgroup of | #13105417, #13105418, #13105420, … |
| maximal normal subgroup of | #13105417, #13105418, #13105420, … |
| maximal quotient of | C5×#64944, C5×#64949, C5×#64953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 787);