Finite Group DatabasebetaFinite Group Databasebeta| order | 800 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×C4⋊AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C5×C4⋊C4) |
| Fitting | C2×C4×C52 ⋊ C4 |
| Sylow | C52 ⋊ C2×C4⋊C4 |
192 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 192 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
140 conjugacy classes — view the full character table.
| maximal subgroup of | #13099790, #13099792, #13099796, … |
| maximal normal subgroup of | #13099790, #13099792, #13099796, … |
| maximal quotient of | C5×D5⋊(C4⋊C8), C5×#65681, C5×#65682, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(800, 1070);