Finite Group DatabasebetaFinite Group Databasebeta| order | 9477 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 314928 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C9 |
| abelian | C9×C13×C81 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator | C1 | G |
| Frattini, cosocle | C3×C27 | C32×C13 |
| socle, prime radical | C32×C13 | C3×C27 |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
98 conjugacy classes of subgroups.
9477 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C9×C13×C81, C9×C13×C243, C13×C27×C81, … |
| maximal normal subgroup of | C2×C9×C13×C81, C9×C13×C243, C13×C27×C81, … |
| maximal quotient of | C2×C9×C13×C81, C9×C13×C243, C13×C27×C81, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9477, 58);