Finite Group DatabasebetaFinite Group Databasebeta| order | 18126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C53⋊AGL(1,𝔽19) |
| unambiguous semidirect product | #4296⋊D53 |
| Fitting, socle, derived, Hall | C19×C53 ⋊ C2×C9 |
| Hall | C53×#4296 ⋊ C2 |
| Hall | D1007 ⋊ C9 |
| Hall | #4296 ⋊ D53 |
| Sylow | C53 ⋊ AGL(1,𝔽19) |
| Sylow | C19 ⋊ C9×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C53 | C2×C9 |
| prime radical | C53⋊(D19⋊C3) | C3 |
| cosocle | C53×C19⋊C3 | C2×C3 |
| LCS | G ▷ C19×C53 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1007 |
Polycyclic presentation:
2,3^2,19,53|b^3=c,d^a=d^18,e^a=e^52,d^b=d^4,d^c=d^7305 conjugacy classes — view the full character table.
| maximal subgroup of | D53×AGL(1,𝔽19), C2×C53⋊AGL(1,𝔽19) |
| maximal normal subgroup of | D53×AGL(1,𝔽19), C2×C53⋊AGL(1,𝔽19) |
| maximal quotient of | #4296⋊Dic53, C2×C53⋊AGL(1,𝔽19) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18126, 15);