Finite Group DatabasebetaFinite Group Databasebeta| order | 4860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | C3×D5×#4183 |
| Fitting, Hall | C3×C5×AΣL(1,𝔽27) ⋊ C22 |
| derived | C5×AΣL(1,𝔽27) ⋊ C22×C3 |
| Sylow | C3×AΣL(1,𝔽27) ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×C3×#4183 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×#4183 |
| commutator, cosocle, hypocenter | C5×AΣL(1,𝔽27) | C22×C3 |
| Frattini | C32 | C3×D5×C3⋊D3 |
| Fitting | C3×C5×AΣL(1,𝔽27) | C22 |
| socle | C32×C5 | C2×#272 |
| LCS | G ▷ C5×AΣL(1,𝔽27) | |
| UCS | C1 ◁ C3 | |
716 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
156 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽5)×#4183, D5×#13091120 |
| maximal normal subgroup of | C3×AGL(1,𝔽5)×#4183 |
Past the SmallGroups library coverage — no SmallGroups id.