Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×D8×AGL(1,𝔽5) |
| Fitting | C52×D8 ⋊ C4 |
| Sylow | C52 ⋊ C4×D8 |
279 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 279 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | C5×AGL(1,𝔽5)×AGL(1,ℤ/8), D8×AGL(1,ℤ/25) |
| maximal normal subgroup of | C5×AGL(1,𝔽5)×AGL(1,ℤ/8) |
| maximal quotient of | D8×AGL(1,ℤ/25) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6842);