Finite Group DatabasebetaFinite Group Databasebeta| order | 4860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C32 |
| direct product | D5×#4207⋊C3 |
| Fitting, Hall | C5×3−1+4 ⋊ C22 |
| derived | C3×C5×C9 ⋊ C22×C32 |
| Sylow | 3−1+4 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×#4207⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×C5×C9 | C22×C32 |
| Frattini | C3 | C32×D5×C3⋊D3 |
| Fitting | C5×3−1+4 | C22 |
| socle | C3×C5 | C2×C32×C3⋊D3 |
| LCS | G ▷ C3×C5×C9 | |
| UCS | C1 | |
812 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 135 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 135 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#4207⋊C3, D5×#13091120, D5×(#4207⋊C2)⋊C3, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#4207⋊C3, D5×(#4207⋊C2)⋊C3, #72254469 |
Past the SmallGroups library coverage — no SmallGroups id.