Finite Group DatabasebetaFinite Group Databasebeta| order | 19458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×D423 |
| unambiguous semidirect product | C9⋊(C23×D47) |
| Fitting, Hall | C9×C23×C47 ⋊ C2 |
| derived, Hall | C9×C47 ⋊ C2×C23 |
| Hall | C23×C47 ⋊ D9 |
| Hall | C9×C23 ⋊ D47 |
| Sylow | C47 ⋊ D9×C23 |
| Sylow | C9 ⋊ C23×D47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D423 |
| commutator, cosocle, hypocenter | C9×C47 | C2×C23 |
| Frattini | C3 | C23×D141 |
| Fitting | C9×C23×C47 | C2 |
| socle | C3×C23×C47 | D3 |
| LCS | G ▷ C9×C47 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9729 |
4899 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19458, 7);