Finite Group DatabasebetaFinite Group Databasebeta| order | 750 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C125 · Schur multiplier (H2) = C1 |
| direct product | D3×C125 |
| unambiguous semidirect product | C3⋊(C2×C125) |
| Fitting, Hall | C3×C125 ⋊ C2 |
| derived, Sylow | C3 ⋊ C2×C125 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C125 | D3 |
| commutator, hypocenter | C3 | C2×C125 |
| Frattini | C25 | C5×D3 |
| Fitting | C3×C125 | C2 |
| socle | C3×C5 | C2×C25 |
| prime radical | C5×D3 | C25 |
| cosocle | C3×C25 | C2×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C125 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 375 |
375 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D125, C2×D3×C125 |
| maximal normal subgroup of | D3×D125, C2×D3×C125 |
| maximal quotient of | Dic3×C125, C2×D3×C125 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(750, 1);