Finite Group DatabasebetaFinite Group Databasebeta| order | 15987 |
| isoclinism | isoclinic class of C73⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C73 · Schur multiplier (H2) = C1 |
| direct product | C73×C73⋊C3 |
| unambiguous semidirect product | C73⋊(C3×C73) |
| Fitting, socle, Sylow | C732 ⋊ C3 |
| derived | C73 ⋊ C3×C73 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C73 | C73⋊C3 |
| commutator, cosocle, hypocenter | C73 | C3×C73 |
| Frattini | C1 | G |
| Fitting, socle | C732 | C3 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C73 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 219 |
1971 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C73×D73⋊C3, (C73⋊C3)⋊D73, D73×C73⋊C3, … |
| maximal normal subgroup of | C73×D73⋊C3, (C73⋊C3)⋊D73, D73×C73⋊C3, … |
| maximal quotient of | C2×C73×C73⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15987, 3);