Finite Group DatabasebetaFinite Group Databasebeta| order | 19683 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 3979430208 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C36 |
| abelian | C33×C729 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C243 | C34 |
| socle, prime radical | C34 | C243 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C243 ▷ C81 ▷ C27 ▷ C9 ▷ C3 ▷ C1 | |
1132 conjugacy classes of subgroups.
19683 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.