Finite Group DatabasebetaFinite Group Databasebeta| order | 3240 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2×C3 |
| direct product | AGL(1,𝔽5)×#4169 |
| Fitting, Hall | C5×C32⋊C9 ⋊ C2×C4 |
| derived | C3×C5×C9 ⋊ C2×C3×C4 |
| Sylow | C32⋊C9 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×#4169 |
264 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 135 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×((C3⋊D3)⋊C9)⋊C2, AGL(1,𝔽5)×#4169⋊C3 |
| maximal normal subgroup of | AGL(1,𝔽5)×((C3⋊D3)⋊C9)⋊C2, AGL(1,𝔽5)×#4169⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.