Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23 |
| direct product | C5×D5⋊#104 |
| unambiguous semidirect product | D5⋊(C5×#104) |
| Fitting | C52×#41 ⋊ C4 |
| Sylow | C52 ⋊ C2×#104 |
360 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 100 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
190 conjugacy classes — view the full character table.
| maximal subgroup of | C5×AGL(1,𝔽5)×#104, C5×#10604863, C5×#10605015, … |
| maximal normal subgroup of | C5×AGL(1,𝔽5)×#104, C5×#10604863, C5×#10605015 |
| maximal quotient of | #72275809 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 6904);