Finite Group DatabasebetaFinite Group Databasebeta| order | 1760 |
| isoclinism | isoclinic class of AGL(1,𝔽11) |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C32 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | (C11⋊C5)⋊C32 |
| unambiguous semidirect product | (C11⋊C32)⋊C5 |
| derived, Sylow | C11 ⋊ C5×C32 |
| Hall | C11⋊C32 ⋊ C5 |
| Hall | C11⋊C5 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C16 | AGL(1,𝔽11) |
| commutator, hypocenter | C11 | C5×C32 |
| Fitting, cosocle | C11×C16 | C2×C5 |
| socle | C2×C11 | C5×C16 |
| prime radical | C2×C11⋊C5 | C16 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C16 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
Polycyclic presentation:
2,5,2^4,11|a^2=c,c^2=d,d^2=e,e^2=f,g^a=g^10,g^b=g^9176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1760, 1);