Finite Group DatabasebetaFinite Group Databasebeta| order | 2430 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | C3×D5×AΣL(1,𝔽27) |
| Fitting, Hall | C3×C5×AΣL(1,𝔽27) ⋊ C2 |
| Sylow | C5 ⋊ C2×C3×AΣL(1,𝔽27) |
504 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 135 |
204 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×AΣL(1,𝔽27), D5×#10624749, C3×D5×#4183, … |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×AΣL(1,𝔽27), D5×#10624749, C3×D5×#4183, … |
Past the SmallGroups library coverage — no SmallGroups id.