Finite Group DatabasebetaFinite Group Databasebeta| order | 4860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | D5×#92259 |
| Fitting, Hall | C5×#6891 ⋊ C22 |
| Sylow | #6891 ⋊ C2×D5 |
| Sylow | C5 ⋊ C2×#92259 |
492 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 79 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
168 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#92259, D5×(((C3⋊D3)⋊C9)⋊C2)⋊C3, #72247462, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#92259, D5×(((C3⋊D3)⋊C9)⋊C2)⋊C3, #72247462 |
Past the SmallGroups library coverage — no SmallGroups id.