Finite Group DatabasebetaFinite Group Databasebeta| order | 18126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C53⋊(D19⋊C3)) |
| unambiguous semidirect product | C53⋊(C3⋊(D19⋊C3)) |
| unambiguous semidirect product | (C19⋊C3)⋊D159 |
| unambiguous semidirect product | D3021⋊C3 |
| Fitting, socle, derived | C3×C19×C53 ⋊ C2×C3 |
| Hall | C3×C53×C19⋊C3 ⋊ C2 |
| Hall | C19×C53 ⋊ C3×D3 |
| Hall | C3×C19⋊C3 ⋊ D53 |
| Sylow | C53 ⋊ C3⋊(D19⋊C3) |
| Sylow | C19 ⋊ C3×D159 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C19×C53 | C2×C3 |
| LCS | G ▷ C3×C19×C53 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3021 |
Polycyclic presentation:
2,3^2,19,53|c^a=c^2,d^a=d^18,e^a=e^52,d^b=d^7720 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18126, 22);