Finite Group DatabasebetaFinite Group Databasebeta| order | 750 |
| isoclinism | isoclinic class of D25⋊C5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C3×D25⋊C5 |
| unambiguous semidirect product | D25⋊(C3×C5) |
| unambiguous semidirect product | 5−1+2⋊(C2×C3) |
| unambiguous semidirect product | (C3×D25)⋊C5 |
| Fitting, Hall | C3×5−1+2 ⋊ C2 |
| derived | C25 ⋊ C2×C3×C5 |
| Sylow | 5−1+2 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D25⋊C5 |
| commutator, cosocle, hypocenter | C25 | C2×C3×C5 |
| Frattini | C5 | C3×C5×D5 |
| Fitting | C3×5−1+2 | C2 |
| socle | C3×C5 | C5×D5 |
| LCS | G ▷ C25 | |
| UCS | C1 ◁ C3 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 75 |
66 conjugacy classes — view the full character table.
| maximal subgroup of | C3×AGL(1,ℤ/25), C3⋊AGL(1,ℤ/25), D3×D25⋊C5, … |
| maximal normal subgroup of | C3×AGL(1,ℤ/25), C3⋊AGL(1,ℤ/25), D3×D25⋊C5, … |
| maximal quotient of | C3×Dic25⋊C5, C2×C3×D25⋊C5, ΓL(1,𝔽8)×D25⋊C5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(750, 11);