Finite Group DatabasebetaFinite Group Databasebeta| order | 10742 |
| isoclinism | isoclinic class of D131 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C41 · Schur multiplier (H2) = C1 |
| direct product | C41×D131 |
| unambiguous semidirect product | C131⋊(C2×C41) |
| Fitting, socle, Hall | C41×C131 ⋊ C2 |
| derived, Sylow | C131 ⋊ C2×C41 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C41 | D131 |
| commutator, cosocle, hypocenter | C131 | C2×C41 |
| Frattini | C1 | G |
| Fitting, socle | C41×C131 | C2 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C41 | |
8 conjugacy classes of subgroups.
2747 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D41×D131, C2×C41×D131, C3×C41×D131, … |
| maximal normal subgroup of | D41×D131, C2×C41×D131, C3×C41×D131 |
| maximal quotient of | C41×Dic131, C2×C41×D131, C3×C41×D131, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10742, 2);