Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26 |
| direct product | C23×Dic11⋊C5 |
| unambiguous semidirect product | (C23×Dic11)⋊C5 |
| derived, Sylow | C11 ⋊ C23×C4×C5 |
| Hall | C23×Dic11 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | AGL(1,𝔽11) |
| commutator, hypocenter | C11 | C23×C4×C5 |
| Frattini | C2 | C23×AGL(1,𝔽11) |
| Fitting, socle | C24×C11 | C2×C5 |
| prime radical | C24×C11⋊C5 | C2 |
| cosocle | C2×C11 | C24×C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C24 | |
472 conjugacy classes of subgroups.
| transitive degree | μt(G) = 352 |
176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1099);