Finite Group DatabasebetaFinite Group Databasebeta| order | 6561 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 5639552984452608 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C37×C93 |
| abelian | C32×C93 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C33 | C35 |
| socle, prime radical | C35 | C33 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
| LECS | G ▷ C33 ▷ C1 | |
60078 conjugacy classes of subgroups.
6561 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C32×C93, C32×C92×C27, C3×C94, … |
| maximal normal subgroup of | C2×C32×C93, C32×C92×C27, C3×C94, … |
| maximal quotient of | C2×C32×C93, C32×C92×C27, C3×C94, … |
Past the SmallGroups library coverage — no SmallGroups id.