Finite Group DatabasebetaFinite Group Databasebeta| order | 9477 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C13 · Schur multiplier (H2) = C3 |
| direct product | C13×#10624526 |
| subgroup | G/H | |
|---|---|---|
| center | C9×C13 | #732 |
| commutator | C3×C9 | C3×C9×C13 |
| Frattini, cosocle | C32×C9 | C32×C13 |
| socle | C3×C13 | H(3,𝔽3)⋊C9 |
| prime radical | C13×#6908 | C3 |
| LCS | G ▷ C3×C9 ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C9×C13 ◁ C3×C9×C13 ◁ C32×C9×C13 ◁ G | |
112 conjugacy classes of subgroups.
1365 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9477, 86);