Finite Group DatabasebetaFinite Group Databasebeta| order | 19458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C9⋊AGL(1,𝔽47) |
| unambiguous semidirect product | D423⋊C23 |
| unambiguous semidirect product | (C47⋊C23)⋊D9 |
| Fitting, derived, Hall | C9×C47 ⋊ C2×C23 |
| Hall | C9×C47⋊C23 ⋊ C2 |
| Hall | C47⋊C23 ⋊ D9 |
| Hall | D423 ⋊ C23 |
| Sylow | C47 ⋊ D9×C23 |
| Sylow | C9 ⋊ AGL(1,𝔽47) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C47 | C2×C23 |
| Frattini | C3 | C3⋊AGL(1,𝔽47) |
| socle | C3×C47 | D3×C23 |
| LCS | G ▷ C9×C47 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 423 |
Polycyclic presentation:
2,3,23,47,3|b^3=e^2,b^a=b^2e,d^a=d^46,e^a=e^2,d^c=d^25147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19458, 12);