Finite Group DatabasebetaFinite Group Databasebeta| order | 15990 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C5⋊((C13⋊C3)⋊D41) |
| unambiguous semidirect product | (C13⋊C3)⋊D205 |
| unambiguous semidirect product | C41⋊(C5⋊(D13⋊C3)) |
| unambiguous semidirect product | D2665⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C5×C13×C41 | C2×C3 |
| LCS | G ▷ C5×C13×C41 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2665 |
Polycyclic presentation:
2,3,5,13,41|c^a=c^4,d^a=d^12,e^a=e^40,d^b=d^3722 conjugacy classes — view the full character table.
| maximal subgroup of | #24922519⋊C3, #24922520⋊C3, #24922523⋊C3, … |
| maximal normal subgroup of | #24922519⋊C3, #24922520⋊C3, #24922523⋊C3, … |
| maximal quotient of | Dic2665⋊C3, C2×C5⋊((C13⋊C3)⋊D41) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15990, 33);