Finite Group DatabasebetaFinite Group Databasebeta| order | 3600 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C4 |
| direct product | AGL(1,𝔽5)×C9⋊AGL(1,𝔽5) |
| Fitting, derived, Hall | C52×C9 ⋊ C42 |
| Sylow | C52 ⋊ C4×Dic9 |
| Sylow | C9 ⋊ AGL(1,𝔽5)2 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C9 | C42 |
| Frattini | C3 | AGL(1,𝔽5)×ΓL(1,𝔽16) |
| socle | C3×C52 | C4×Dic3 |
| prime radical | C3×D52 | C2×D3 |
| cosocle | C9×D52 | C22 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 | |
189 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 189 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
105 conjugacy classes — view the full character table.
| maximal subgroup of | D9×AGL(1,𝔽5)2, AGL(1,𝔽5)×3−1+2⋊AGL(1,𝔽5) |
| maximal normal subgroup of | D9×AGL(1,𝔽5)2, AGL(1,𝔽5)×3−1+2⋊AGL(1,𝔽5) |
Past the SmallGroups library coverage — no SmallGroups id.