Finite Group DatabasebetaFinite Group Databasebeta| order | 35090 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×D1595 |
| unambiguous semidirect product | C5⋊(C11×D319) |
| unambiguous semidirect product | C11⋊(C11×D145) |
| unambiguous semidirect product | C29⋊(C11×D55) |
| Fitting, socle, Hall | C5×C112×C29 ⋊ C2 |
| derived | C5×C11×C29 ⋊ C2×C11 |
| Hall | C112×C29 ⋊ D5 |
| Hall | C5×C112 ⋊ D29 |
| Hall | C5×C29 ⋊ C11×D11 |
| Sylow | C112 ⋊ D145 |
| Sylow | C29 ⋊ C11×D55 |
| Sylow | C5 ⋊ C11×D319 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | D1595 |
| commutator, cosocle, hypocenter | C5×C11×C29 | C2×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C112×C29 | C2 |
| LCS | G ▷ C5×C11×C29 | |
| UCS | C1 ◁ C11 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3190 |
8789 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35090, 52);