Finite Group DatabasebetaFinite Group Databasebeta| order | 10340 |
| isoclinism | isoclinic class of AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11×C47 · Schur multiplier (H2) = C1 |
| direct product | C11×AGL(1,𝔽5)×C47 |
| Fitting, socle, Hall | C5×C11×C47 ⋊ C4 |
| derived, Sylow | C5 ⋊ C4×C11×C47 |
| Hall | C5×C47 ⋊ C4×C11 |
| Hall | C5×C11 ⋊ C4×C47 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11×C47 | AGL(1,𝔽5) |
| commutator, hypocenter | C5 | C4×C11×C47 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C47 | C4 |
| prime radical | D5×C11×C47 | C2 |
| cosocle | D5 | C2×C11×C47 |
| LCS | G ▷ C5 | |
| UCS | C1 ◁ C11×C47 | |
24 conjugacy classes of subgroups.
2585 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C11×AGL(1,𝔽5)×C47, C11×C47×ΓL(1,𝔽16) |
| maximal normal subgroup of | C3×C11×AGL(1,𝔽5)×C47 |
| maximal quotient of | C3×C11×AGL(1,𝔽5)×C47, C11×C47×ΓL(1,𝔽16) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10340, 20);