Finite Group DatabasebetaFinite Group Databasebeta| order | 4374 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C33 |
| direct product | C9×#92303 |
| Fitting, Sylow | C9×C9⋊H(3,𝔽3) ⋊ C2 |
| derived | C32×C9 ⋊ C2×C3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | #92303 |
| commutator, hypocenter | C32×C9 | C2×C3×C9 |
| Frattini, socle | C33 | C32×C3⋊D3 |
| Fitting | C9×C9⋊H(3,𝔽3) | C2 |
| prime radical | C3×#92303 | C3 |
| cosocle | C33×C9 | C2×C32 |
| LCS | G ▷ C32×C9 | |
| UCS | C1 ◁ C9 | |
1033 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
270 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72243916, C9×D9⋊((C3⋊D3)⋊C3), D9×#92303, … |
| maximal normal subgroup of | #72243916, C9×D9⋊((C3⋊D3)⋊C3), D9×#92303, … |
Past the SmallGroups library coverage — no SmallGroups id.