Finite Group DatabasebetaFinite Group Databasebeta| order | 19683 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order ≥ 263 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C320×C9 |
| abelian | C35×C92 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C32 | C37 |
| socle, prime radical | C37 | C32 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C32 ▷ C1 | |
11870872 conjugacy classes of subgroups.
19683 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.