Finite Group DatabasebetaFinite Group Databasebeta| order | 9477 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C13 · Schur multiplier (H2) = C32 |
| direct product | C13×#10624481 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C13 | #732 |
| commutator, Frattini, cosocle | C32×C9 | C32×C13 |
| prime radical | C3×C13×#732 | C3 |
| LCS | G ▷ C32×C9 ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C13 ◁ C33×C13 ◁ C32×C9×C13 ◁ G | |
144 conjugacy classes of subgroups; only the 32 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 32 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
741 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9477, 41);