Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | D5×#611⋊C3 |
| Fitting | C22×C5×3−1+2 ⋊ C22 |
| Hall | C5×3−1+2 ⋊ C2×D4 |
| Sylow | 3−1+2 ⋊ D4×D5 |
| Sylow | C5 ⋊ C2×#611⋊C3 |
356 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 83 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#611⋊C3, D4×D5×AGL(1,ℤ/9), #72247459, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#611⋊C3, D4×D5×AGL(1,ℤ/9), #72247459 |
| maximal quotient of | #72254700, #72254724, D5×#63694⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.