Finite Group DatabasebetaFinite Group Databasebeta| order | 15717 |
| isoclinism | isoclinic class of C31⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C132 · Schur multiplier (H2) = C13 |
| direct product | C132×C31⋊C3 |
| unambiguous semidirect product | C31⋊(C3×C132) |
| Fitting, socle, Hall | C132×C31 ⋊ C3 |
| derived, Sylow | C31 ⋊ C3×C132 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C132 | C31⋊C3 |
| commutator, cosocle, hypocenter | C31 | C3×C132 |
| Frattini | C1 | G |
| Fitting, socle | C132×C31 | C3 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C132 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5239 |
2197 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C132×D31⋊C3, C13×(C31⋊C3)⋊D13, C13×D13×C31⋊C3, … |
| maximal normal subgroup of | C132×D31⋊C3, C13×(C31⋊C3)⋊D13, C13×D13×C31⋊C3, … |
| maximal quotient of | C2×C132×C31⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15717, 15);