Finite Group DatabasebetaFinite Group Databasebeta| order | 17514 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3 |
| direct product | C3×C7×D139⋊C3 |
| unambiguous semidirect product | D139⋊(C32×C7) |
| unambiguous semidirect product | (C139⋊C3)⋊(C2×C3×C7) |
| unambiguous semidirect product | (C3×D139)⋊(C3×C7) |
| Fitting, socle | C3×C7×C139 ⋊ C2×C3 |
| derived, Sylow | C139 ⋊ C2×C32×C7 |
| Hall | C3×C7×C139⋊C3 ⋊ C2 |
| Hall | C7×D139 ⋊ C32 |
| Hall | C3×C139⋊C3 ⋊ C2×C7 |
| Hall | C7×C139 ⋊ C2×C32 |
| Hall | D139 ⋊ C32×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7 | D139⋊C3 |
| commutator, cosocle, hypocenter | C139 | C2×C32×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C139 | C2×C3 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C3×C7 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2919 |
609 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D7×D139⋊C3, D3×C7×D139⋊C3, D21×D139⋊C3, … |
| maximal normal subgroup of | C3×D7×D139⋊C3, D3×C7×D139⋊C3, D21×D139⋊C3, … |
| maximal quotient of | C3×C7×(C139⋊C3)⋊C4, C2×C3×C7×D139⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17514, 30);