Finite Group DatabasebetaFinite Group Databasebeta| order | 2400 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26×C5 |
| direct product | C2×D12×C5⋊D5 |
| Fitting | C2×C3×C4×C52 ⋊ C22 |
| Hall | C3×C52 ⋊ C22×D4 |
| Sylow | C52 ⋊ C22×D12 |
| Sylow | C3 ⋊ C2×D4×C5⋊D5 |
1888 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 1888 conjugacy classes of subgroups — too many to draw. Only its 294 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 600 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(6,7,8,9)(15,16,18,19,17);(4,5)(10,11,13,14,12);(11,12)(13,14)(16,17)(18,19);(2,3)(7,9)252 conjugacy classes — view the full character table.
Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:
gap> G := Group((1,2,3)(6,7,8,9)(15,16,18,19,17), (4,5)(10,11,13,14,12), (11,12)(13,14)(16,17)(18,19), (2,3)(7,9));