Finite Group DatabasebetaFinite Group Databasebeta| order | 3200 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29×C5 |
| direct product | C2×#13104938 |
| Fitting | C25×C52 ⋊ C4 |
| Sylow | C52 ⋊ C2×#379 |
12578 conjugacy classes of subgroups; only the 462 normal subgroups are shown.
This group has 12578 conjugacy classes of subgroups — too many to draw. Only its 462 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 20 |
| transitive degree | μt(G) = 80 |
A minimal faithful permutation representation — 4 generators on 20 points:
(1,2,5,3,4)(6,7,8,10,9)(11,12);(14,16);(18,20);(2,3,4,5)(7,8,9,10)(13,14)(15,16)(17,18)(19,20)248 conjugacy classes — view the full character table.
| maximal quotient of | #72226429, #72226461, #72226551 |
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,5,3,4)(6,7,8,10,9)(11,12), (14,16), (18,20), (2,3,4,5)(7,8,9,10)(13,14)(15,16)(17,18)(19,20));