Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| isoclinism | isoclinic class of D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C1 |
| direct product | C3×C23×D75 |
| unambiguous semidirect product | C3⋊(C3×C23×D25) |
| unambiguous semidirect product | C25⋊(C3×D3×C23) |
| Fitting, Hall | C32×C23×C25 ⋊ C2 |
| derived | C3×C25 ⋊ C2×C3×C23 |
| Hall | C23×C25 ⋊ C3×D3 |
| Hall | C32×C25 ⋊ C2×C23 |
| Hall | C32×C23 ⋊ D25 |
| Sylow | C25 ⋊ C3×D3×C23 |
| Sylow | C32 ⋊ C23×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | D75 |
| commutator, cosocle, hypocenter | C3×C25 | C2×C3×C23 |
| Frattini | C5 | C3×C23×D15 |
| Fitting | C32×C23×C25 | C2 |
| socle | C32×C5×C23 | D5 |
| LCS | G ▷ C3×C25 | |
| UCS | C1 ◁ C3×C23 | |
54 conjugacy classes of subgroups.
2691 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D23×D75, C3×D3×C23×D25, C3×D69⋊D25, … |
| maximal normal subgroup of | C3×D23×D75, C3×D3×C23×D25, C3×D69⋊D25, … |
| maximal quotient of | C3×C23×Dic75, C2×C3×C23×D75 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 15);