Finite Group DatabasebetaFinite Group Databasebeta| order | 15717 |
| isoclinism | isoclinic class of #92788 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C31 · Schur multiplier (H2) = C1 |
| direct product | C31×#92788 |
| Fitting, socle, Hall | C132×C31 ⋊ C3 |
| derived, Sylow | C132 ⋊ C3×C31 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C31 | #92788 |
| commutator, cosocle, hypocenter | C132 | C3×C31 |
| Frattini | C1 | G |
| Fitting, socle | C132×C31 | C3 |
| LCS | G ▷ C132 | |
| UCS | C1 ◁ C31 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5239 |
1829 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D31×#92788, C31×#11759815, #44537663, … |
| maximal normal subgroup of | D31×#92788, C31×#11759815, #44537663, … |
| maximal quotient of | C2×C31×#92788 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15717, 14);