Finite Group DatabasebetaFinite Group Databasebeta| order | 6561 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C35 · Schur multiplier (H2) = C37 |
| direct product | 3−1+2×#6900 |
| subgroup | G/H | |
|---|---|---|
| center, commutator, Frattini, socle, cosocle | C33 | C35 |
| prime radical | C35 | C33 |
| LCS | G ▷ C33 ▷ C1 | |
| UCS | C1 ◁ C33 ◁ G | |
| LECS | G ▷ C33 ▷ C1 | |
10106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 729 |
561 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | 3−1+2×#92314, AGL(1,ℤ/9)×#6900, #72243235, … |
| maximal subgroup of | 3−1+2×#92314, AGL(1,ℤ/9)×#6900, #72243235, … |
| maximal normal subgroup of | 3−1+2×#92314, AGL(1,ℤ/9)×#6900, #72243235, … |
Past the SmallGroups library coverage — no SmallGroups id.