Finite Group DatabasebetaFinite Group Databasebeta| order | 10731 |
| isoclinism | isoclinic class of C73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C49 · Schur multiplier (H2) = C1 |
| direct product | C49×C73⋊C3 |
| unambiguous semidirect product | C73⋊(C3×C49) |
| Fitting, Hall | C49×C73 ⋊ C3 |
| derived, Sylow | C73 ⋊ C3×C49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C49 | C73⋊C3 |
| commutator, hypocenter | C73 | C3×C49 |
| Frattini | C7 | C7×C73⋊C3 |
| Fitting | C49×C73 | C3 |
| socle, cosocle | C7×C73 | C3×C7 |
| prime radical | C7×C73⋊C3 | C7 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C49 | |
12 conjugacy classes of subgroups.
1323 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C49×C73⋊C3, C49×D73⋊C3, D49×C73⋊C3, … |
| maximal normal subgroup of | C2×C49×C73⋊C3, C49×D73⋊C3, D49×C73⋊C3, … |
| maximal quotient of | C2×C49×C73⋊C3, C49×#10620321, C3×C49×C73⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10731, 3);