Finite Group DatabasebetaFinite Group Databasebeta| order | 9531 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C353 · Schur multiplier (H2) = C1 |
| direct product | 3−1+2×C353 |
| unambiguous semidirect product | C9⋊(C3×C353) |
| unambiguous semidirect product | (C9×C353)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C3×C353 | C32 |
| commutator, Frattini, cosocle | C3 | C32×C353 |
| prime radical | C32×C353 | C3 |
| LCS | G ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C3×C353 ◁ G | |
16 conjugacy classes of subgroups.
3883 conjugacy classes. The character table is too large to display.
| maximal subgroup of | AΣL(1,𝔽27)×C353, #731×C353, #733×C353, … |
| maximal normal subgroup of | AΣL(1,𝔽27)×C353, #731×C353, #733×C353, … |
| maximal quotient of | C32⋊C9×C353, C9⋊C9×C353, C3×3−1+2×C353 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9531, 4);