Finite Group DatabasebetaFinite Group Databasebeta| order | 15990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D39×C41⋊C5 |
| unambiguous semidirect product | C3⋊(D13×C41⋊C5) |
| unambiguous semidirect product | C13⋊(D3×C41⋊C5) |
| unambiguous semidirect product | (C41×D39)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C13×C41 | C2×C5 |
| LCS | G ▷ C3×C13×C41 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1599 |
273 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D39×D41⋊C5, D39⋊(D41⋊C5), D3×D13×C41⋊C5, … |
| maximal normal subgroup of | D39×D41⋊C5, D39⋊(D41⋊C5), D3×D13×C41⋊C5, … |
| maximal quotient of | Dic39×C41⋊C5, C2×D39×C41⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15990, 25);