Finite Group DatabasebetaFinite Group Databasebeta| order | 35226 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C19 · Schur multiplier (H2) = C1 |
| direct product | C19×D927 |
| unambiguous semidirect product | C9⋊(C19×D103) |
| unambiguous semidirect product | C103⋊(D9×C19) |
| Fitting, Hall | C9×C19×C103 ⋊ C2 |
| derived, Hall | C9×C103 ⋊ C2×C19 |
| Hall | C19×C103 ⋊ D9 |
| Hall | C9×C19 ⋊ D103 |
| Sylow | C103 ⋊ D9×C19 |
| Sylow | C9 ⋊ C19×D103 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C19 | D927 |
| commutator, cosocle, hypocenter | C9×C103 | C2×C19 |
| Frattini | C3 | C19×D309 |
| Fitting | C9×C19×C103 | C2 |
| socle | C3×C19×C103 | D3 |
| LCS | G ▷ C9×C103 | |
| UCS | C1 ◁ C19 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17613 |
8835 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35226, 10);