Finite Group DatabasebetaFinite Group Databasebeta| order | 5400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C5 · Schur multiplier (H2) = C23 |
| direct product | C2×C5×D5×AGL(1,ℤ/9) |
| Fitting | C2×C52×3−1+2 ⋊ C22 |
| derived | C5×C9 ⋊ C23×C3×C5 |
| Hall | C52×3−1+2 ⋊ C23 |
| Sylow | 3−1+2 ⋊ C22×C5×D5 |
| Sylow | C52 ⋊ C22×AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | D5×AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C5×C9 | C23×C3×C5 |
| Frattini | C3 | C2×C3×C5×D3×D5 |
| Fitting | C2×C52×3−1+2 | C22 |
| socle | C2×C3×C52 | C2×C3×D3 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C2×C5 | |
468 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 126 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×D52×AGL(1,ℤ/9), C5×C22⋊D5×AGL(1,ℤ/9), AGL(1,ℤ/9)×#6038 |
| maximal normal subgroup of | C2×D52×AGL(1,ℤ/9), C5×C22⋊D5×AGL(1,ℤ/9), AGL(1,ℤ/9)×#6038 |
| maximal quotient of | C5×C22⋊D5×AGL(1,ℤ/9) |
Past the SmallGroups library coverage — no SmallGroups id.