Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| isoclinism | isoclinic class of D5×D11 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×D5×D11 |
| unambiguous semidirect product | (D5×C11)⋊C24 |
| unambiguous semidirect product | (C5×D11)⋊C24 |
| unambiguous semidirect product | D55⋊C24 |
| Fitting, socle | C23×C5×C11 ⋊ C22 |
| derived, Hall | C5×C11 ⋊ C25 |
| Sylow | C11 ⋊ C24×D5 |
| Sylow | C5 ⋊ C24×D11 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D5×D11 |
| commutator, cosocle, hypocenter | C5×C11 | C25 |
| Frattini | C1 | G |
| Fitting, socle | C23×C5×C11 | C22 |
| LCS | G ▷ C5×C11 | |
| UCS | C1 ◁ C23 | |
1496 conjugacy classes of subgroups.
| transitive degree | μt(G) = 440 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1281);