Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23×C3 |
| direct product | C32×D5×#67 |
| Fitting | C22×C33×C5 ⋊ C22 |
| Hall | C33×C5 ⋊ C2×D4 |
| Sylow | C33 ⋊ D4×D5 |
| Sylow | C5 ⋊ C2×C32×#67 |
904 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
324 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D5×#3811, C32×AGL(1,𝔽5)×#67, C3×#67⋊ΓL(1,𝔽16) |
| maximal normal subgroup of | C3×D5×#3811, C32×AGL(1,𝔽5)×#67, C3×#67⋊ΓL(1,𝔽16) |
Past the SmallGroups library coverage — no SmallGroups id.