Finite Group DatabasebetaFinite Group Databasebeta| order | 15990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊(C13⋊(D41⋊C5)) |
| unambiguous semidirect product | C13⋊(C3⋊(D41⋊C5)) |
| unambiguous semidirect product | (C41⋊C5)⋊D39 |
| unambiguous semidirect product | D1599⋊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 |
Polycyclic presentation:
2,3,5,13,41|b^a=b^2,d^a=d^12,e^a=e^40,e^c=e^10261 conjugacy classes — view the full character table.
| maximal subgroup of | D39×D41⋊C5, D13×C3⋊(D41⋊C5), D3×C13⋊(D41⋊C5), … |
| maximal normal subgroup of | D39×D41⋊C5, D13×C3⋊(D41⋊C5), D3×C13⋊(D41⋊C5), … |
| maximal quotient of | C3⋊(Dic533⋊C5), C2×C3⋊(C13⋊(D41⋊C5)) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15990, 26);