Finite Group DatabasebetaFinite Group Databasebeta| order | 19683 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4132485216 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C32×C81 |
| abelian | C3×C812 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C272 | C33 |
| socle, prime radical | C33 | C272 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C272 ▷ C92 ▷ C32 ▷ C1 | |
1402 conjugacy classes of subgroups.
19683 conjugacy classes. The character table is too large to display.
Past the SmallGroups library coverage — no SmallGroups id.