Finite Group DatabasebetaFinite Group Databasebeta| order | 17514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D2919 |
| unambiguous semidirect product | C3⋊(C3×D973) |
| Fitting, socle, Hall | C32×C7×C139 ⋊ C2 |
| derived | C3×C7×C139 ⋊ C2×C3 |
| Hall | C32×C139 ⋊ D7 |
| Hall | C7×C139 ⋊ C3×D3 |
| Sylow | C139 ⋊ C3×D21 |
| Hall | C32×C7 ⋊ D139 |
| Sylow | C32 ⋊ D973 |
| Sylow | C7 ⋊ C3×D417 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D2919 |
| commutator, cosocle, hypocenter | C3×C7×C139 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C7×C139 | C2 |
| LCS | G ▷ C3×C7×C139 | |
| UCS | C1 ◁ C3 | |
36 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5838 |
4383 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D21×D139, C3×D7×D417, C3×D3×D973, … |
| maximal normal subgroup of | C3×D21×D139, C3×D7×D417, C3×D3×D973, … |
| maximal quotient of | C3×Dic2919, C2×C3×D2919 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17514, 66);