Finite Group DatabasebetaFinite Group Databasebeta| order | 6480 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | AGL(1,𝔽5)×((C3⋊D3)⋊C9)⋊C2 |
| Fitting, derived, Hall | C5×C32⋊C9 ⋊ C22×C4 |
| Sylow | C32⋊C9 ⋊ C22×AGL(1,𝔽5) |
| Sylow | C5 ⋊ C4×((C3⋊D3)⋊C9)⋊C2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C32⋊C9 | C22×C4 |
| Frattini | C32 | D32×AGL(1,𝔽5) |
| socle | C32×C5 | C4×D32 |
| prime radical | D5×((C3⋊D3)⋊C9)⋊C2 | C2 |
| cosocle | D5×C32⋊C9 | C23 |
| LCS | G ▷ C5×C32⋊C9 | |
| UCS | C1 | |
690 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 690 conjugacy classes of subgroups — too many to draw. Only its 78 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×(((C3⋊D3)⋊C9)⋊C2)⋊C3 |
| maximal normal subgroup of | AGL(1,𝔽5)×(((C3⋊D3)⋊C9)⋊C2)⋊C3 |
Past the SmallGroups library coverage — no SmallGroups id.