Finite Group DatabasebetaFinite Group Databasebeta| order | 15717 |
| isoclinism | isoclinic class of C169⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×C169⋊C3 |
| unambiguous semidirect product | C169⋊(C3×C31) |
| Fitting, Hall | C31×C169 ⋊ C3 |
| derived, Sylow | C169 ⋊ C3×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | C169⋊C3 |
| commutator, cosocle, hypocenter | C169 | C3×C31 |
| Frattini | C13 | C31×C13⋊C3 |
| Fitting | C31×C169 | C3 |
| socle | C13×C31 | C13⋊C3 |
| LCS | G ▷ C169 | |
| UCS | C1 ◁ C31 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5239 |
1829 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C31×C169⋊C3, D31×C169⋊C3, C31×D169⋊C3, … |
| maximal normal subgroup of | C2×C31×C169⋊C3, D31×C169⋊C3, C31×D169⋊C3, … |
| maximal quotient of | C2×C31×C169⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15717, 2);