Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of (C2×AGL(1,𝔽5))⋊D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#87825 |
| unambiguous semidirect product | D5⋊#683 |
| Sylow | C52 ⋊ C2×C4⋊C4 |
192 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #13103286, AGL(1,𝔽5)×#683, #13103605, … |
| maximal normal subgroup of | #13103286, AGL(1,𝔽5)×#683, #13103605, … |
| maximal quotient of | #13103474, D5⋊#3946, #13103570, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1000);