Finite Group DatabasebetaFinite Group Databasebeta| order | 2550 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C25 · Schur multiplier (H2) = C1 |
| direct product | D3×C17×C25 |
| unambiguous semidirect product | C3⋊(C2×C17×C25) |
| Fitting, Hall | C3×C17×C25 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C17×C25 |
| Hall | C3×C25 ⋊ C2×C17 |
| Hall | C3×C17 ⋊ C2×C25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17×C25 | D3 |
| commutator, hypocenter | C3 | C2×C17×C25 |
| Frattini | C5 | C5×D3×C17 |
| Fitting | C3×C17×C25 | C2 |
| socle | C3×C5×C17 | C2×C5 |
| prime radical | C5×D3×C17 | C5 |
| cosocle | C3×C5 | C2×C5×C17 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C17×C25 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1275 |
A minimal faithful permutation representation — 2 generators on 45 points:
(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(2,3)1275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×C7×C17×C25, C17×C25×D21, D3×C11×C17×C25, … |
| maximal normal subgroup of | D3×C7×C17×C25, D3×C11×C17×C25, D3×C13×C17×C25 |
| maximal quotient of | D3×C7×C17×C25, C17×C25×D21, D3×C11×C17×C25, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2550, 5);