Finite Group DatabasebetaFinite Group Databasebeta| order | 1500 |
| isoclinism | isoclinic class of D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C125 · Schur multiplier (H2) = C2 |
| direct product | C2×D3×C125 |
| unambiguous semidirect product | C3⋊(C22×C125) |
| unambiguous semidirect product | (C2×C3)⋊(C2×C125) |
| Fitting | C2×C3×C125 ⋊ C2 |
| derived, Sylow | C3 ⋊ C22×C125 |
| Hall | C3×C125 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C125 | D3 |
| commutator, hypocenter | C3 | C22×C125 |
| Frattini | C25 | C2×C5×D3 |
| Fitting | C2×C3×C125 | C2 |
| socle | C2×C3×C5 | C2×C25 |
| prime radical | C2×C5×D3 | C25 |
| cosocle | C3×C25 | C22×C5 |
| LCS | G ▷ C3 | |
| UCS | C1 ◁ C2×C125 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 750 |
750 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1500, 10);