Finite Group DatabasebetaFinite Group Databasebeta| order | 4860 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2 |
| direct product | C5×(((C3⋊D3)⋊C9)⋊C2)⋊C3 |
| Fitting, Hall | C5×#6891 ⋊ C22 |
| derived | C32⋊C9 ⋊ C22×C3×C5 |
| Sylow | #6891 ⋊ C22×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | (((C3⋊D3)⋊C9)⋊C2)⋊C3 |
| commutator, cosocle, hypocenter | C32⋊C9 | C22×C3×C5 |
| Frattini | C32 | C3×C5×D32 |
| Fitting | C5×#6891 | C22 |
| socle | C32×C5 | C3×D32 |
| LCS | G ▷ C32⋊C9 | |
| UCS | C1 ◁ C5 | |
368 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
195 conjugacy classes — view the full character table.
| maximal subgroup of | D5×(((C3⋊D3)⋊C9)⋊C2)⋊C3 |
| maximal normal subgroup of | D5×(((C3⋊D3)⋊C9)⋊C2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.