Finite Group DatabasebetaFinite Group Databasebeta| order | 750 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C1 |
| direct product | D3×5−1+2 |
| unambiguous semidirect product | C3⋊(C2×5−1+2) |
| unambiguous semidirect product | (D3×C25)⋊C5 |
| Fitting, Hall | C3×5−1+2 ⋊ C2 |
| Sylow | C3 ⋊ C2×5−1+2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C5 | C52×D3 |
| commutator, socle, cosocle | C3×C5 | C2×C52 |
| Fitting | C3×5−1+2 | C2 |
| prime radical | C52×D3 | C5 |
| hypercenter | 5−1+2 | D3 |
| hypocenter | C3 | C2×5−1+2 |
| LCS | G ▷ C3×C5 ▷ C3 | |
| UCS | C1 ◁ C5 ◁ 5−1+2 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 75 |
87 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D25⋊C5, C2×D3×5−1+2, S4×5−1+2, … |
| maximal normal subgroup of | D3×D25⋊C5, C2×D3×5−1+2, C3×D3×5−1+2 |
| maximal quotient of | Dic3×5−1+2, C2×D3×5−1+2, S4×5−1+2, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(750, 16);