Finite Group DatabasebetaFinite Group Databasebeta| order | 19458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9×C23 · Schur multiplier (H2) = C1 |
| direct product | C9×AGL(1,𝔽47) |
| unambiguous semidirect product | D47⋊(C9×C23) |
| unambiguous semidirect product | (C9×D47)⋊C23 |
| unambiguous semidirect product | (C47⋊C23)⋊(C2×C9) |
| Fitting, Hall | C9×C47 ⋊ C2×C23 |
| derived, Sylow | C47 ⋊ C2×C9×C23 |
| Hall | C9×C47⋊C23 ⋊ C2 |
| Hall | C47⋊C23 ⋊ C2×C9 |
| Hall | C9×D47 ⋊ C23 |
| Hall | D47 ⋊ C9×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C9 | AGL(1,𝔽47) |
| commutator, hypocenter | C47 | C2×C9×C23 |
| Frattini | C3 | C3×AGL(1,𝔽47) |
| Fitting | C9×C47 | C2×C23 |
| socle, cosocle | C3×C47 | C2×C3×C23 |
| prime radical | C3×AGL(1,𝔽47) | C3 |
| LCS | G ▷ C47 | |
| UCS | C1 ◁ C9 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 423 |
423 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19458, 10);