Finite Group DatabasebetaFinite Group Databasebeta| order | 35140 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C7⋊(Dic251⋊C5) |
| unambiguous semidirect product | (C251⋊C5)⋊Dic7 |
| unambiguous semidirect product | Dic1757⋊C5 |
| derived, Hall | C7×C251 ⋊ C4×C5 |
| Hall | C7×C251⋊C5 ⋊ C4 |
| Hall | Dic1757 ⋊ C5 |
| Hall | C251⋊C5 ⋊ Dic7 |
| Sylow | C251 ⋊ C5×Dic7 |
| Sylow | C7 ⋊ Dic251⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | C7⋊(D251⋊C5) |
| commutator, hypocenter | C7×C251 | C4×C5 |
| Fitting, socle, cosocle | C2×C7×C251 | C2×C5 |
| prime radical | C2×C7×C251⋊C5 | C2 |
| LCS | G ▷ C7×C251 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 7028 |
Polycyclic presentation:
2,5,7,251,2|a^2=e,c^a=c^6,d^a=d^250,d^b=d^219400 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35140, 12);