Finite Group DatabasebetaFinite Group Databasebeta| order | 3240 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | D9×C9⋊AGL(1,𝔽5) |
| Fitting, derived, Hall | C5×C92 ⋊ C2×C4 |
| Sylow | C92 ⋊ C2×AGL(1,𝔽5) |
| Sylow | C5 ⋊ D9×Dic9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C5×C92 | C2×C4 |
| Frattini | C32 | D3×ΓL(1,𝔽16) |
| socle | C32×C5 | D3×Dic3 |
| prime radical | C3×D5×D9 | D3 |
| cosocle | C92×D5 | C22 |
| LCS | G ▷ C5×C92 | |
| UCS | C1 | |
186 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
126 conjugacy classes — view the full character table.
| maximal subgroup of | #72222406, D92×AGL(1,𝔽5) |
| maximal normal subgroup of | #72222406, D92×AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.