Finite Group DatabasebetaFinite Group Databasebeta| order | 4860 |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C4 · Schur multiplier (H2) = C33 |
| direct product | C3×AGL(1,𝔽5)×AΣL(1,𝔽27) |
| Fitting, Hall | C3×C5×AΣL(1,𝔽27) ⋊ C4 |
| Sylow | C5 ⋊ C3×C4×AΣL(1,𝔽27) |
756 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 756 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 135 |
255 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#10624749, C3×AGL(1,𝔽5)×#4183 |
| maximal normal subgroup of | AGL(1,𝔽5)×#10624749, C3×AGL(1,𝔽5)×#4183 |
Past the SmallGroups library coverage — no SmallGroups id.