Finite Group DatabasebetaFinite Group Databasebeta| order | 2160 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×PSU(3,𝔽2)⋊D5 |
| Fitting, socle, Hall | C33×C5 ⋊ SD16 |
| Sylow | C33 ⋊ #688 |
| Sylow | C5 ⋊ C3×AΓL(1,𝔽9) |
108 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 108 conjugacy classes of subgroups — too many to draw. Only its 26 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
63 conjugacy classes — view the full character table.
| maximal subgroup of | C3×D5×AΓL(1,𝔽9), C3×#72213709, C2×C3×PSU(3,𝔽2)⋊D5 |
| maximal normal subgroup of | C3×D5×AΓL(1,𝔽9), C2×C3×PSU(3,𝔽2)⋊D5 |
| maximal quotient of | C2×C3×PSU(3,𝔽2)⋊D5 |
Past the SmallGroups library coverage — no SmallGroups id.