Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| isoclinism | isoclinic class of C3⋊D75 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C23 · Schur multiplier (H2) = C3 |
| direct product | C23×C3⋊D75 |
| unambiguous semidirect product | C3⋊(C23×D75) |
| unambiguous semidirect product | C25⋊(C3⋊D3×C23) |
| Fitting, Hall | C32×C23×C25 ⋊ C2 |
| derived, Hall | C32×C25 ⋊ C2×C23 |
| Hall | C23×C25 ⋊ C3⋊D3 |
| Hall | C32×C23 ⋊ D25 |
| Sylow | C25 ⋊ C3⋊D3×C23 |
| Sylow | C32 ⋊ C23×D25 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | C3⋊D75 |
| commutator, cosocle, hypocenter | C32×C25 | C2×C23 |
| Frattini | C5 | C23×C3⋊D15 |
| Fitting | C32×C23×C25 | C2 |
| socle | C32×C5×C23 | D5 |
| LCS | G ▷ C32×C25 | |
| UCS | C1 ◁ C23 | |
72 conjugacy classes of subgroups.
2622 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×C3⋊D75, C3⋊D3×C23×D25, D575⋊(C3⋊D3), … |
| maximal normal subgroup of | D23×C3⋊D75, C3⋊D3×C23×D25, D575⋊(C3⋊D3), … |
| maximal quotient of | C23×C3⋊Dic75, C2×C23×C3⋊D75 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 19);