Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C42 · Schur multiplier (H2) = C4 |
| direct product | C3×Dic3×ΓL(1,𝔽16) |
| derived | C32×C5 ⋊ C3×C42 |
| Hall | C33×C5 ⋊ C42 |
| Sylow | C33 ⋊ C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×Dic32 |
356 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
162 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×#624, ΓL(1,𝔽16)×#624, C3×D3×Dic3×AGL(1,𝔽5), … |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×#624, ΓL(1,𝔽16)×#624, C3×D3×Dic3×AGL(1,𝔽5), … |
Past the SmallGroups library coverage — no SmallGroups id.