Finite Group DatabasebetaFinite Group Databasebeta| order | 15759 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C17 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C103 ⋊ C3×C17 |
| derived, Sylow | C103 ⋊ C32×C17 |
| Hall | C103⋊C17 ⋊ C32 |
| Hall | C3×C103⋊C3 ⋊ C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C103⋊C3)⋊C17 |
| commutator, cosocle, hypocenter | C103 | C32×C17 |
| Frattini | C1 | G |
| Fitting, socle | C3×C103 | C3×C17 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 309 |
159 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,𝔽103), C3⋊AGL(1,𝔽103), D3×(C103⋊C3)⋊C17, … |
| maximal normal subgroup of | C3×AGL(1,𝔽103), C3⋊AGL(1,𝔽103), D3×(C103⋊C3)⋊C17, … |
| maximal quotient of | C2×C3×(C103⋊C3)⋊C17 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15759, 6);