Finite Group DatabasebetaFinite Group Databasebeta| order | 3240 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C2×C32 |
| direct product | D5×A4×3−1+2 |
| Fitting | C22×C5×3−1+2 ⋊ C2×C3 |
| Hall | C22×D5 ⋊ C3×3−1+2 |
| Sylow | C5 ⋊ C2×A4×3−1+2 |
368 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#13049240, A4×AGL(1,𝔽5)×3−1+2, D5×A4×AGL(1,ℤ/9), … |
| maximal normal subgroup of | A4×AGL(1,𝔽5)×3−1+2, D5×A4×AGL(1,ℤ/9), A4×3−1+2⋊AGL(1,𝔽5), … |
| maximal quotient of | D5×#13049240 |
Past the SmallGroups library coverage — no SmallGroups id.