Finite Group DatabasebetaFinite Group Databasebeta| order | 15810 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D51×ΓL(1,𝔽32) |
| unambiguous semidirect product | C3⋊(D17×ΓL(1,𝔽32)) |
| unambiguous semidirect product | C17⋊(D3×ΓL(1,𝔽32)) |
| unambiguous semidirect product | (C31×D51)⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C3×C17×C31 | C2×C5 |
| LCS | G ▷ C3×C17×C31 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1581 |
297 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D51×D31⋊C5, D51⋊(D31⋊C5), D3×D17×ΓL(1,𝔽32), … |
| maximal normal subgroup of | D51×D31⋊C5, D51⋊(D31⋊C5), D3×D17×ΓL(1,𝔽32), … |
| maximal quotient of | ΓL(1,𝔽32)×Dic51, C2×D51×ΓL(1,𝔽32) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15810, 25);