Finite Group DatabasebetaFinite Group Databasebeta| order | 19683 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) = C2×C6561 (order 13122) · Inn(G) = C1 · Out(G) = C2×C6561 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C1 |
| cyclic | C19683 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C6561 | C3 |
| socle, prime radical | C3 | C6561 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C6561 ▷ C2187 ▷ C729 ▷ C243 ▷ C81 ▷ C27 ▷ C9 ▷ C3 ▷ C1 | |
10 conjugacy classes of subgroups.
19683 conjugacy classes. The character table is too large to display.
| derived subgroup of | D19683 |
| Fitting subgroup of | D19683 |
| maximal subgroup of | D19683 |
| maximal normal subgroup of | D19683 |
Past the SmallGroups library coverage — no SmallGroups id.