Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | D5×#689 |
| Sylow | C52 ⋊ C2×Q16 |
138 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#689, #13103749, #13103750, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#689, #13103749, #13103750, … |
| maximal quotient of | #13100594, #13100620, #13100621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 719);