Finite Group DatabasebetaFinite Group Databasebeta| order | 11421 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9×C47 · Schur multiplier (H2) = C32 |
| direct product | C47×H(3,𝔽3)⋊C9 |
| unambiguous semidirect product | H(3,𝔽3)⋊(C9×C47) |
| unambiguous semidirect product | (H(3,𝔽3)×C47)⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C47 | H(3,𝔽3) |
| commutator | C32 | C3×C9×C47 |
| Frattini, cosocle | C33 | C32×C47 |
| prime radical | C3×H(3,𝔽3)×C47 | C3 |
| LCS | G ▷ C32 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C32×C47 ◁ C33×C47 ◁ G | |
94 conjugacy classes of subgroups.
2397 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(11421, 17);