Finite Group DatabasebetaFinite Group Databasebeta| order | 4374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C32 |
| direct product | C9×#92314 |
| Fitting, Sylow | C9×#6900 ⋊ C2 |
| derived | C92 ⋊ C2×C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #92314 |
| commutator, hypocenter | C92 | C2×C3×C9 |
| Frattini, socle | C33 | C32×C3⋊D3 |
| Fitting | C9×#6900 | C2 |
| prime radical | C3×#92314 | C3 |
| cosocle | C3×C92 | C2×C32 |
| LCS | G ▷ C92 | |
| UCS | C1 ◁ C9 | |
940 conjugacy classes of subgroups.
| transitive degree | μt(G) = 486 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | 3−1+2×#92314, D9×#92314, C9×#92265⋊C2, … |
| maximal normal subgroup of | 3−1+2×#92314, D9×#92314, C9×#92265⋊C2, … |
Past the SmallGroups library coverage — no SmallGroups id.