Finite Group DatabasebetaFinite Group Databasebeta| order | 17570 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | D7×C251⋊C5 |
| unambiguous semidirect product | C7⋊(C2×C251⋊C5) |
| unambiguous semidirect product | (D7×C251)⋊C5 |
| Fitting, socle, derived, Hall | C7×C251 ⋊ C2×C5 |
| Hall | C7×C251⋊C5 ⋊ C2 |
| Hall | D7×C251 ⋊ C5 |
| Sylow | C251 ⋊ C5×D7 |
| Sylow | C7 ⋊ C2×C251⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C7×C251 | C2×C5 |
| LCS | G ▷ C7×C251 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1757 |
275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D7×D251⋊C5, C2×D7×C251⋊C5 |
| maximal normal subgroup of | D7×D251⋊C5, C2×D7×C251⋊C5 |
| maximal quotient of | Dic7×C251⋊C5, C2×D7×C251⋊C5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17570, 11);