Finite Group DatabasebetaFinite Group Databasebeta| order | 19458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×D3×C47⋊C23 |
| unambiguous semidirect product | C3⋊(C2×C3×C47⋊C23) |
| unambiguous semidirect product | (D3×C47)⋊(C3×C23) |
| unambiguous semidirect product | (C3×D3×C47)⋊C23 |
| Fitting, socle, Hall | C32×C47 ⋊ C2×C23 |
| derived | C3×C47 ⋊ C2×C3×C23 |
| Hall | C32×C47⋊C23 ⋊ C2 |
| Hall | C3×D3×C47 ⋊ C23 |
| Sylow | C47 ⋊ C3×D3×C23 |
| Sylow | C32 ⋊ C2×C47⋊C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D3×C47⋊C23 |
| commutator, cosocle, hypocenter | C3×C47 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C32×C47 | C2×C23 |
| LCS | G ▷ C3×C47 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 282 |
225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19458, 16);