Finite Group DatabasebetaFinite Group Databasebeta| order | 9477 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C13 · Schur multiplier (H2) = C32 |
| direct product | C13×#10624475 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C13 | #6856 |
| commutator, Frattini, cosocle | C34 | C32×C13 |
| prime radical | C13×C32⋊H(3,𝔽3) | C3 |
| LCS | G ▷ C34 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C13 ◁ C33×C13 ◁ C34×C13 ◁ G | |
196 conjugacy classes of subgroups.
533 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9477, 35);