Finite Group DatabasebetaFinite Group Databasebeta| order | 1950 |
| isoclinism | isoclinic class of D39 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C25 · Schur multiplier (H2) = C1 |
| direct product | C25×D39 |
| unambiguous semidirect product | C3⋊(C25×D13) |
| unambiguous semidirect product | C13⋊(D3×C25) |
| Fitting, Hall | C3×C13×C25 ⋊ C2 |
| derived, Hall | C3×C13 ⋊ C2×C25 |
| Hall | C13×C25 ⋊ D3 |
| Hall | C3×C25 ⋊ D13 |
| Sylow | C13 ⋊ D3×C25 |
| Sylow | C3 ⋊ C25×D13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D39 |
| commutator, hypocenter | C3×C13 | C2×C25 |
| Frattini | C5 | C5×D39 |
| Fitting | C3×C13×C25 | C2 |
| socle, cosocle | C3×C5×C13 | C2×C5 |
| prime radical | C5×D39 | C5 |
| LCS | G ▷ C3×C13 | |
| UCS | C1 ◁ C25 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 975 |
A minimal faithful permutation representation — 2 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25)(26,27,28)(29,30,31,32,33,34,35,36,37,38,39,40,41);(27,28)(30,41)(31,40)(32,39)(33,38)(34,37)(35,36)525 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C25×D13, D25×D39, D39⋊D25, … |
| maximal normal subgroup of | D3×C25×D13, D25×D39, D39⋊D25, … |
| maximal quotient of | C25×Dic39, C2×C25×D39, C7×C25×D39, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1950, 9);