Finite Group DatabasebetaFinite Group Databasebeta| order | 5400 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23 |
| direct product | C2×D5×C5⋊AGL(1,ℤ/9) |
| Fitting | C2×C52×3−1+2 ⋊ C22 |
| derived | C52×C9 ⋊ C23×C3 |
| Hall | C52×3−1+2 ⋊ C23 |
| Sylow | 3−1+2 ⋊ C2×D52 |
| Sylow | C52 ⋊ C22×AGL(1,ℤ/9) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×C5⋊AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C52×C9 | C23×C3 |
| Frattini | C3 | C2×C3×D5×D15 |
| Fitting | C2×C52×3−1+2 | C22 |
| socle | C2×C3×C52 | C2×C3×D3 |
| LCS | G ▷ C52×C9 | |
| UCS | C1 ◁ C2 | |
468 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
256 conjugacy classes — view the full character table.
| maximal subgroup of | C2×D52×AGL(1,ℤ/9), #72254766, #72254771 |
| maximal normal subgroup of | C2×D52×AGL(1,ℤ/9), #72254766, #72254771 |
| maximal quotient of | #72254766 |
Past the SmallGroups library coverage — no SmallGroups id.