Finite Group DatabasebetaFinite Group Databasebeta| order | 15620 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×C71⋊AGL(1,𝔽5) |
| unambiguous semidirect product | C71⋊(C11×AGL(1,𝔽5)) |
| Fitting, socle, Hall | C5×C11×C71 ⋊ C4 |
| derived, Hall | C5×C71 ⋊ C4×C11 |
| Hall | C11×C71 ⋊ AGL(1,𝔽5) |
| Sylow | C71 ⋊ C11×AGL(1,𝔽5) |
| Hall | C5×C11 ⋊ Dic71 |
| Sylow | C5 ⋊ C11×Dic71 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C11 | C71⋊AGL(1,𝔽5) |
| commutator, hypocenter | C5×C71 | C4×C11 |
| Frattini | C1 | G |
| Fitting, socle | C5×C11×C71 | C4 |
| prime radical | D5×C11×C71 | C2 |
| cosocle | D5×C71 | C2×C11 |
| LCS | G ▷ C5×C71 | |
| UCS | C1 ◁ C11 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3905 |
1595 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15620, 66);