Finite Group DatabasebetaFinite Group Databasebeta| order | 15717 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C169 · Schur multiplier (H2) = C1 |
| direct product | C31⋊C3×C169 |
| unambiguous semidirect product | C31⋊(C3×C169) |
| Fitting, Hall | C31×C169 ⋊ C3 |
| derived, Sylow | C31 ⋊ C3×C169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C169 | C31⋊C3 |
| commutator, hypocenter | C31 | C3×C169 |
| Frattini | C13 | C13×C31⋊C3 |
| Fitting | C31×C169 | C3 |
| socle, cosocle | C13×C31 | C3×C13 |
| prime radical | C13×C31⋊C3 | C13 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C169 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5239 |
2197 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C31⋊C3×C169, C169×D31⋊C3, C31⋊C3×D169, … |
| maximal normal subgroup of | C2×C31⋊C3×C169, C169×D31⋊C3, C31⋊C3×D169, … |
| maximal quotient of | C2×C31⋊C3×C169 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15717, 3);