Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
| direct product | AGL(1,𝔽5)×Dic10 |
| unambiguous semidirect product | (C5×AGL(1,𝔽5))⋊Q8 |
| Sylow | C52 ⋊ C4×Q8 |
146 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
65 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#677, #13103441, AGL(1,𝔽5)×Dic20, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#677, #13103441, AGL(1,𝔽5)×Dic20, … |
| maximal quotient of | #13103472, #170×Dic10, #13103481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 981);