Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×(C2×D3)⋊ΓL(1,𝔽16) |
| Hall | C33×C5 ⋊ C22⋊C4 |
| Sylow | C33 ⋊ C22⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C3×(C2×D3)⋊Dic3 |
420 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
144 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#13088405, C3×#67⋊ΓL(1,𝔽16), C3×AGL(1,𝔽5)×#626, … |
| maximal normal subgroup of | C3×#13088405, C3×#67⋊ΓL(1,𝔽16), C3×AGL(1,𝔽5)×#626, … |
Past the SmallGroups library coverage — no SmallGroups id.