Finite Group DatabasebetaFinite Group Databasebeta| order | 36252 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4296⋊#6157 |
| Fitting, socle, derived, Hall | C19×C53 ⋊ C4×C9 |
| Hall | C53×#4296 ⋊ C4 |
| Hall | C19⋊#6157 ⋊ C9 |
| Hall | #4296 ⋊ #6157 |
| Sylow | C53 ⋊ #4296⋊C4 |
| Sylow | C19 ⋊ C9×#6157 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C19×C53 | C4×C9 |
| prime radical, cosocle | C19⋊C3×D53 | C2×C3 |
| LCS | G ▷ C19×C53 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1007 |
Polycyclic presentation:
2,3,2,3,19,53|a^2=c,b^3=d,e^a=e^18,f^a=f^30,e^b=e^4,f^c=f^52,e^d=e^7181 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36252, 66);