Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #686 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#3964 |
| Sylow | C52 ⋊ #102 |
154 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 50 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×#3964, #13101584, #13101585, … |
| maximal normal subgroup of | D5×#3964, #13101584, #13101585, … |
| maximal quotient of | C5×#64749, C5×D4⋊#168, C5×#64757, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 317);