Finite Group DatabasebetaFinite Group Databasebeta| order | 4374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C3 |
| direct product | D9×#6900 |
| Fitting, Sylow | C9×#6900 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center | C32 | C33×D9 |
| commutator, cosocle | C32×C9 | C2×C33 |
| Frattini, socle | C33 | C33×D3 |
| Fitting | C9×#6900 | C2 |
| prime radical | C33×D9 | C32 |
| hypercenter | #6900 | D9 |
| hypocenter | C9 | C2×#6900 |
| LCS | G ▷ C32×C9 ▷ C9 | |
| UCS | C1 ◁ C32 ◁ #6900 | |
910 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 910 conjugacy classes of subgroups — too many to draw. Only its 180 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 486 |
306 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AGL(1,ℤ/9)×#6900, D9×#92314, D9×#92265 |
| maximal normal subgroup of | AGL(1,ℤ/9)×#6900, D9×#92314, D9×#92265 |
Past the SmallGroups library coverage — no SmallGroups id.