Finite Group DatabasebetaFinite Group Databasebeta| order | 18126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D3021 |
| unambiguous semidirect product | C19⋊(C3⋊D159) |
| unambiguous semidirect product | C53⋊(C3⋊D57) |
| Fitting, socle, derived, Hall | C32×C19×C53 ⋊ C2 |
| Hall | C19×C53 ⋊ C3⋊D3 |
| Hall | C32×C53 ⋊ D19 |
| Hall | C32×C19 ⋊ D53 |
| Sylow | C53 ⋊ C3⋊D57 |
| Sylow | C19 ⋊ C3⋊D159 |
| Sylow | C32 ⋊ D1007 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C19×C53 | C2 |
| LCS | G ▷ C32×C19×C53 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9063 |
Polycyclic presentation:
2,3^2,19,53|b^a=b^2,c^a=c^2,d^a=d^18,e^a=e^524533 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D3021, D57×D159, D53×C3⋊D57, … |
| maximal normal subgroup of | D3×D3021, D57×D159, D53×C3⋊D57, … |
| maximal quotient of | C3⋊Dic3021, C2×C3⋊D3021 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18126, 26);