Finite Group DatabasebetaFinite Group Databasebeta| order | 19458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊(C3⋊AGL(1,𝔽47)) |
| unambiguous semidirect product | (C3⋊D141)⋊C23 |
| unambiguous semidirect product | (C47⋊C23)⋊(C3⋊D3) |
| Fitting, socle, derived, Hall | C32×C47 ⋊ C2×C23 |
| Hall | C32×C47⋊C23 ⋊ C2 |
| Hall | C47⋊C23 ⋊ C3⋊D3 |
| Hall | C3⋊D141 ⋊ C23 |
| Sylow | C47 ⋊ C3⋊D3×C23 |
| Sylow | C32 ⋊ AGL(1,𝔽47) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C47 | C2×C23 |
| LCS | G ▷ C32×C47 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 423 |
Polycyclic presentation:
2,23,3^2,47|c^a=c^2,d^a=d^2,e^a=e^46,e^b=e^25147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19458, 17);