Finite Group DatabasebetaFinite Group Databasebeta| order | 20511 |
| automorphism | ? |
| homology | Abelianization (H1) = C9×C53 · Schur multiplier (H2) = C1 |
| direct product | C53×C43⋊C9 |
| unambiguous semidirect product | C43⋊(C9×C53) |
| unambiguous semidirect product | (C43×C53)⋊C9 |
| derived, Sylow | C43 ⋊ C9×C53 |
| Hall | C43×C53 ⋊ C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C53 | C43⋊C3 |
| commutator, hypocenter | C43 | C9×C53 |
| Frattini | C3 | C53×C43⋊C3 |
| Fitting, socle, prime radical | C3×C43×C53 | C3 |
| cosocle | C3×C43 | C3×C53 |
| LCS | G ▷ C43 | |
| UCS | C1 ◁ C3×C53 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20511 |
2703 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20511, 2);