Finite Group DatabasebetaFinite Group Databasebeta| order | 5184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C25×C3 |
| direct product | C2×C22⋊A4×AGL(1,ℤ/9) |
| Fitting | C25×3−1+2 ⋊ C2×C3 |
| derived | C24×C9 ⋊ C22×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C22⋊A4×AGL(1,ℤ/9) |
| commutator, cosocle, hypocenter | C24×C9 | C22×C32 |
| Frattini | C3 | C2×C3×D3×C22⋊A4 |
| Fitting | C25×3−1+2 | C2×C3 |
| socle | C25×C3 | C32×D3 |
| LCS | G ▷ C24×C9 | |
| UCS | C1 ◁ C2 | |
6470 conjugacy classes of subgroups; only the 142 normal subgroups are shown.
This group has 6470 conjugacy classes of subgroups — too many to draw. Only its 142 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
160 conjugacy classes — view the full character table.
| maximal quotient of | C2×AGL(1,ℤ/9)×#997 |
Past the SmallGroups library coverage — no SmallGroups id.