Finite Group DatabasebetaFinite Group Databasebeta| order | 15785 |
| isoclinism | isoclinic class of C11⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C7×C41 · Schur multiplier (H2) = C1 |
| direct product | C7×C41×C11⋊C5 |
| unambiguous semidirect product | C11⋊(C5×C7×C41) |
| unambiguous semidirect product | (C7×C11)⋊(C5×C41) |
| Fitting, socle, Hall | C7×C11×C41 ⋊ C5 |
| derived, Sylow | C11 ⋊ C5×C7×C41 |
| Hall | C11×C41 ⋊ C5×C7 |
| Hall | C7×C11 ⋊ C5×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7×C41 | C11⋊C5 |
| commutator, cosocle, hypocenter | C11 | C5×C7×C41 |
| Frattini | C1 | G |
| Fitting, socle | C7×C11×C41 | C5 |
| LCS | G ▷ C11 | |
| UCS | C1 ◁ C7×C41 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3157 |
2009 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C7×C41×C11⋊C5, C7×C11⋊C5×D41, C7×C41×AGL(1,𝔽11), … |
| maximal normal subgroup of | C2×C7×C41×C11⋊C5, C7×C11⋊C5×D41, C7×C41×AGL(1,𝔽11), … |
| maximal quotient of | C2×C7×C41×C11⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15785, 3);