Finite Group DatabasebetaFinite Group Databasebeta| order | 19182 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(D139⋊C23) |
| unambiguous semidirect product | D417⋊C23 |
| unambiguous semidirect product | (C139⋊C23)⋊D3 |
| Fitting, socle, derived, Hall | C3×C139 ⋊ C2×C23 |
| Hall | C3×C139⋊C23 ⋊ C2 |
| Hall | C139⋊C23 ⋊ D3 |
| Hall | D417 ⋊ C23 |
| Sylow | C139 ⋊ D3×C23 |
| Sylow | C3 ⋊ D139⋊C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C139 | C2×C23 |
| LCS | G ▷ C3×C139 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,23,139|b^a=b^2,d^a=d^138,d^c=d^6478 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D139⋊C23, C2×C3⋊(D139⋊C23) |
| maximal normal subgroup of | D3×D139⋊C23, C2×C3⋊(D139⋊C23) |
| maximal quotient of | C3⋊(Dic139⋊C23), C2×C3⋊(D139⋊C23) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19182, 14);