Finite Group DatabasebetaFinite Group Databasebeta| order | 35820 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×D5×#13184226 |
| unambiguous semidirect product | C5⋊(C22×#13184226) |
| unambiguous semidirect product | (C2×C5)⋊(C2×#13184226) |
| Fitting, socle | C2×C5×C199 ⋊ C2×C9 |
| derived, Hall | C5×C199 ⋊ C22×C9 |
| Hall | C5×#13184226 ⋊ C22 |
| Hall | C2×D5×C199 ⋊ C9 |
| Sylow | C199 ⋊ C2×C9×D5 |
| Sylow | C5 ⋊ C22×#13184226 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D5×#13184226 |
| commutator, hypocenter | C5×C199 | C22×C9 |
| Frattini | C1 | G |
| Fitting, socle | C2×C5×C199 | C2×C9 |
| prime radical | C2×D5×C199⋊C3 | C3 |
| cosocle | C5×C199⋊C3 | C22×C3 |
| LCS | G ▷ C5×C199 | |
| UCS | C1 ◁ C2 | |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1990 |
248 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35820, 71);