Finite Group DatabasebetaFinite Group Databasebeta| order | 19182 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| affine general linear | AGL(1,𝔽139) |
| unambiguous semidirect product | (D139⋊C3)⋊C23 |
| unambiguous semidirect product | (D139⋊C23)⋊C3 |
| unambiguous semidirect product | ((C139⋊C3)⋊C23)⋊C2 |
| Fitting, socle, derived, Sylow | C139 ⋊ C2×C3×C23 |
| Hall | (C139⋊C3)⋊C23 ⋊ C2 |
| Hall | D139⋊C23 ⋊ C3 |
| Hall | C139⋊C23 ⋊ C2×C3 |
| Hall | D139⋊C3 ⋊ C23 |
| Hall | C139⋊C3 ⋊ C2×C23 |
| Hall | D139 ⋊ C3×C23 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C139 | C2×C3×C23 |
| LCS | G ▷ C139 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,23,139|d^a=d^138,d^b=d^96,d^c=d^64139 conjugacy classes — view the full character table.
| maximal subgroup of | C2×AGL(1,𝔽139) |
| maximal normal subgroup of | C2×AGL(1,𝔽139) |
| maximal quotient of | ((C139⋊C3)⋊C4)⋊C23, C2×AGL(1,𝔽139) |
| holomorph of | C139 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19182, 18);