Finite Group DatabasebetaFinite Group Databasebeta| order | 6450 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C43 · Schur multiplier (H2) = C1 |
| direct product | C43×D75 |
| unambiguous semidirect product | C3⋊(C43×D25) |
| unambiguous semidirect product | C25⋊(D3×C43) |
| Fitting, Hall | C3×C25×C43 ⋊ C2 |
| derived, Hall | C3×C25 ⋊ C2×C43 |
| Hall | C25×C43 ⋊ D3 |
| Hall | C3×C43 ⋊ D25 |
| Sylow | C25 ⋊ D3×C43 |
| Sylow | C3 ⋊ C43×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C43 | D75 |
| commutator, hypocenter | C3×C25 | C2×C43 |
| Frattini | C5 | D15×C43 |
| Fitting | C3×C25×C43 | C2 |
| socle | C3×C5×C43 | D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C43 | |
24 conjugacy classes of subgroups.
1677 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D43×D75, D3×C43×D25, D75⋊D43, … |
| maximal normal subgroup of | D43×D75, D3×C43×D25, D75⋊D43, … |
| maximal quotient of | C43×Dic75, C2×C43×D75, C43×D225, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6450, 11);