Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C42 · Schur multiplier (H2) = C3×C4 |
| direct product | C32×Dic3×AGL(1,𝔽5) |
| derived | C3×C5 ⋊ C32×C42 |
| Hall | C33×C5 ⋊ C42 |
| Sylow | C33 ⋊ C4×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C32×C4×Dic3 |
488 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×AGL(1,𝔽5)×#624, C3×D3×Dic3×AGL(1,𝔽5), AGL(1,𝔽5)×#6289, … |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×#624, C3×D3×Dic3×AGL(1,𝔽5), AGL(1,𝔽5)×#6289, … |
Past the SmallGroups library coverage — no SmallGroups id.