Finite Group DatabasebetaFinite Group Databasebeta| order | 2590 |
| isoclinism | isoclinic class of D259 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×D259 |
| unambiguous semidirect product | C7⋊(C5×D37) |
| unambiguous semidirect product | C37⋊(C5×D7) |
| Fitting, socle, Hall | C5×C7×C37 ⋊ C2 |
| derived, Hall | C7×C37 ⋊ C2×C5 |
| Hall | C5×C37 ⋊ D7 |
| Sylow | C37 ⋊ C5×D7 |
| Hall | C5×C7 ⋊ D37 |
| Sylow | C7 ⋊ C5×D37 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | D259 |
| commutator, cosocle, hypocenter | C7×C37 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C37 | C2 |
| LCS | G ▷ C7×C37 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1295 |
655 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C25×D259, C5×D1295, C52×D259, … |
| maximal normal subgroup of | C25×D259, C52×D259, C5×C7×D259, … |
| maximal quotient of | C25×D259, C5×D1295, C52×D259, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2590, 4);