Finite Group DatabasebetaFinite Group Databasebeta| order | 19440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,𝔽5)×#92265⋊C2 |
| Fitting, Hall | C5×#6900 ⋊ C22×C4 |
| derived | C5×C92 ⋊ C22×C3×C4 |
| Sylow | #6900 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×#92265⋊C2 |
1310 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 1310 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
180 conjugacy classes — view the full character table.
| holomorph of | C5×D9 |
Past the SmallGroups library coverage — no SmallGroups id.