Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24 |
| direct product | C5×D5×#99 |
| Fitting | C52×#99 ⋊ C2 |
| Sylow | C52 ⋊ C2×#99 |
472 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 106 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | C5×AGL(1,𝔽5)×#99, C5×D5×B(4,𝔽2), C5×#10603919, … |
| maximal normal subgroup of | C5×AGL(1,𝔽5)×#99, C5×D5×B(4,𝔽2), C5×#10603919 |
| maximal quotient of | #99×D25⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4356);