Finite Group DatabasebetaFinite Group Databasebeta| order | 19182 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C23⋊(D139⋊C3) |
| unambiguous semidirect product | (C139⋊C3)⋊D23 |
| unambiguous semidirect product | D3197⋊C3 |
| Fitting, socle, derived, Hall | C23×C139 ⋊ C2×C3 |
| Hall | C23×C139⋊C3 ⋊ C2 |
| Hall | D3197 ⋊ C3 |
| Hall | C139⋊C3 ⋊ D23 |
| Sylow | C139 ⋊ C3×D23 |
| Sylow | C23 ⋊ D139⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C23×C139 | C2×C3 |
| LCS | G ▷ C23×C139 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,23,139|c^a=c^22,d^a=d^138,d^b=d^96568 conjugacy classes — view the full character table.
| maximal subgroup of | D23×D139⋊C3, C2×C23⋊(D139⋊C3) |
| maximal normal subgroup of | D23×D139⋊C3, C2×C23⋊(D139⋊C3) |
| maximal quotient of | C23⋊((C139⋊C3)⋊C4), C2×C23⋊(D139⋊C3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19182, 17);