Finite Group DatabasebetaFinite Group Databasebeta| order | 5400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C52 · Schur multiplier (H2) = C23×C5 |
| direct product | C22×C52×AGL(1,ℤ/9) |
| Fitting | C22×C52×3−1+2 ⋊ C2 |
| derived | C9 ⋊ C23×C3×C52 |
| Hall | C52×3−1+2 ⋊ C23 |
| Sylow | 3−1+2 ⋊ C23×C52 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C52 | AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C9 | C23×C3×C52 |
| Frattini | C3 | C22×C3×C52×D3 |
| Fitting | C22×C52×3−1+2 | C2 |
| socle | C22×C3×C52 | C3×D3 |
| LCS | G ▷ C9 | |
| UCS | C1 ◁ C22×C52 | |
808 conjugacy classes of subgroups; only the 376 normal subgroups are shown.
This group has 808 conjugacy classes of subgroups — too many to draw. Only its 376 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 900 |
1000 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C22×C5⋊D5×AGL(1,ℤ/9), C5×C22⋊D5×AGL(1,ℤ/9) |
| maximal normal subgroup of | C22×C5⋊D5×AGL(1,ℤ/9), C5×C22⋊D5×AGL(1,ℤ/9) |
Past the SmallGroups library coverage — no SmallGroups id.