Finite Group DatabasebetaFinite Group Databasebeta| order | 35820 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #13184226⋊AGL(1,𝔽5) |
| Fitting, socle, derived, Hall | C5×C199 ⋊ C4×C9 |
| Hall | C5×#13184226 ⋊ C4 |
| Hall | C199⋊AGL(1,𝔽5) ⋊ C9 |
| Hall | #13184226 ⋊ AGL(1,𝔽5) |
| Sylow | C199 ⋊ C9×AGL(1,𝔽5) |
| Sylow | C5 ⋊ #13184226⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C199 | C4×C9 |
| prime radical, cosocle | D5×C199⋊C3 | C2×C3 |
| LCS | G ▷ C5×C199 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 995 |
Polycyclic presentation:
2,3,2,3,5,199|a^2=c,b^3=d,e^a=e^2,f^a=f^198,f^b=f^162,e^c=e^4,f^d=f^9289 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35820, 66);