Finite Group DatabasebetaFinite Group Databasebeta| order | 15717 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×#11925881 |
| Fitting, socle, Hall | C132×C31 ⋊ C3 |
| derived | C13×C31 ⋊ C3×C13 |
| Sylow | C132 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ C13×C13⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | #11925881 |
| commutator, cosocle, hypocenter | C13×C31 | C3×C13 |
| Frattini | C1 | G |
| Fitting, socle | C132×C31 | C3 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 ◁ C13 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1209 |
1781 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×#14559023, C13×#14559031, C13×#14559027, … |
| maximal normal subgroup of | C13×#14559023, C13×#14559031, C13×#14559027, … |
| maximal quotient of | C2×C13×#11925881 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15717, 9);