Finite Group DatabasebetaFinite Group Databasebeta| order | 750 |
| isoclinism | isoclinic class of D125 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D125 |
| unambiguous semidirect product | C125⋊(C2×C3) |
| Fitting, Hall | C3×C125 ⋊ C2 |
| derived, Sylow | C125 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D125 |
| commutator, cosocle, hypocenter | C125 | C2×C3 |
| Frattini | C25 | C3×D5 |
| Fitting | C3×C125 | C2 |
| socle | C3×C5 | D25 |
| LCS | G ▷ C125 | |
| UCS | C1 ◁ C3 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 375 |
192 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#92517, C3⋊#92517, D3×D125, … |
| maximal normal subgroup of | C3×#92517, C3⋊#92517, D3×D125, … |
| maximal quotient of | C3×Dic125, C2×C3×D125 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(750, 2);