Finite Group DatabasebetaFinite Group Databasebeta| order | 18126 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C53⋊(#4294⋊C2) |
| unambiguous semidirect product | #4294⋊D53 |
| derived, Hall | C19×C53 ⋊ C2×C9 |
| Hall | C53×#4294 ⋊ C2 |
| Hall | D1007 ⋊ C9 |
| Hall | #4294 ⋊ D53 |
| Sylow | C53 ⋊ #4294⋊C2 |
| Sylow | C19 ⋊ C9×D53 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | C53⋊(D19⋊C3) |
| commutator, hypocenter | C19×C53 | C2×C9 |
| Fitting, socle, cosocle | C3×C19×C53 | C2×C3 |
| prime radical | C3×D1007 | C3 |
| LCS | G ▷ C19×C53 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9063 |
Polycyclic presentation:
2,3,19,53,3|b^3=e,c^a=c^18,d^a=d^52,c^b=c^7729 conjugacy classes — view the full character table.
| maximal subgroup of | D53×#4294⋊C2, C2×C53⋊(#4294⋊C2) |
| maximal normal subgroup of | D53×#4294⋊C2, C2×C53⋊(#4294⋊C2) |
| maximal quotient of | #4294⋊Dic53, C2×C53⋊(#4294⋊C2) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18126, 12);