Finite Group DatabasebetaFinite Group Databasebeta| order | 17598 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×D1257 |
| unambiguous semidirect product | C3⋊(C7×D419) |
| unambiguous semidirect product | C419⋊(D3×C7) |
| Fitting, socle, Hall | C3×C7×C419 ⋊ C2 |
| derived, Hall | C3×C419 ⋊ C2×C7 |
| Hall | C7×C419 ⋊ D3 |
| Sylow | C419 ⋊ D3×C7 |
| Hall | C3×C7 ⋊ D419 |
| Sylow | C3 ⋊ C7×D419 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D1257 |
| commutator, cosocle, hypocenter | C3×C419 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C7×C419 | C2 |
| LCS | G ▷ C3×C419 | |
| UCS | C1 ◁ C7 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8799 |
4410 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×D419, D7×D1257, D21⋊D419, … |
| maximal normal subgroup of | D3×C7×D419, D7×D1257, D21⋊D419, … |
| maximal quotient of | C7×Dic1257, C2×C7×D1257 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17598, 7);