Finite Group DatabasebetaFinite Group Databasebeta| order | 1600 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C5 |
| direct product | #100×C5⋊D5 |
| Fitting | C52×#100 ⋊ C2 |
| Sylow | C52 ⋊ C2×#100 |
744 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 125 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 200 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | C5⋊D5×#453, #72221215, #100×#1043, … |
| maximal normal subgroup of | C5⋊D5×#453, #72221215, #100×#1043, … |
| maximal quotient of | C2×#100×C5⋊D5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1600, 4959);