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) = C24 |
| direct product | C2×(C2×AGL(1,𝔽5))⋊D5 |
| unambiguous semidirect product | D5⋊#685 |
| Sylow | C52 ⋊ C2×C22⋊C4 |
280 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 280 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) = 80 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | #13103284, #13103609, C4×(C2×AGL(1,𝔽5))⋊D5, … |
| maximal normal subgroup of | #13103284, #13103609, C4×(C2×AGL(1,𝔽5))⋊D5, … |
| maximal quotient of | #13103472, #13103475, D5⋊#3952, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 999);