Finite Group DatabasebetaFinite Group Databasebeta| order | 15717 |
| isoclinism | isoclinic class of C13⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13×C31 · Schur multiplier (H2) = C1 |
| direct product | C13×C31×C13⋊C3 |
| unambiguous semidirect product | C13⋊(C3×C13×C31) |
| Fitting, socle, Hall | C132×C31 ⋊ C3 |
| derived | C13 ⋊ C3×C13×C31 |
| Sylow | C132 ⋊ C3×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13×C31 | C13⋊C3 |
| commutator, cosocle, hypocenter | C13 | C3×C13×C31 |
| Frattini | C1 | G |
| Fitting, socle | C132×C31 | C3 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C13×C31 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1209 |
2821 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×C13⋊C3×D31, C13×C31×D13⋊C3, C13×(C13⋊C3)⋊D31, … |
| maximal normal subgroup of | C13×C13⋊C3×D31, C13×C31×D13⋊C3, C13×(C13⋊C3)⋊D31, … |
| maximal quotient of | C2×C13×C31×C13⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15717, 11);