Finite Group DatabasebetaFinite Group Databasebeta| order | 35820 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C9 · Schur multiplier (H2) = C2 |
| direct product | C5×C22⋊#13184226 |
| unambiguous semidirect product | C22⋊(C5×#13184226) |
| unambiguous semidirect product | (C22×C5)⋊#13184226 |
| Fitting, socle, Hall | C22×C5×C199 ⋊ C9 |
| derived, Hall | C22×C199 ⋊ C5×C9 |
| Hall | C5×C199 ⋊ C22⋊C9 |
| Sylow | C199 ⋊ C5×C22⋊C9 |
| Hall | C22×C5 ⋊ #13184226 |
| Sylow | C22 ⋊ C5×#13184226 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | C22⋊#13184226 |
| commutator, hypocenter | C22×C199 | C5×C9 |
| Frattini | C1 | G |
| Fitting, socle | C22×C5×C199 | C9 |
| prime radical | C22×C5×C199⋊C3 | C3 |
| cosocle | C22×C199⋊C3 | C3×C5 |
| LCS | G ▷ C22×C199 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3980 |
500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35820, 83);