Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1725 |
| unambiguous semidirect product | C23⋊(C3⋊D75) |
| unambiguous semidirect product | C25⋊(C3⋊D69) |
| Fitting, derived, Hall | C32×C23×C25 ⋊ C2 |
| Hall | C23×C25 ⋊ C3⋊D3 |
| Hall | C32×C25 ⋊ D23 |
| Hall | C32×C23 ⋊ D25 |
| Sylow | C25 ⋊ C3⋊D69 |
| Sylow | C23 ⋊ C3⋊D75 |
| Sylow | C32 ⋊ D575 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C32×C23×C25 | C2 |
| Frattini | C5 | C3⋊D345 |
| socle | C32×C5×C23 | D5 |
| LCS | G ▷ C32×C23×C25 | |
| UCS | C1 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,23,5|d^5=f^4,b^a=b^2,c^a=c^2,d^a=d^4f,e^a=e^22,f^a=f^42589 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×C3⋊D75, D25×C3⋊D69, C3⋊D3×D575, … |
| maximal normal subgroup of | D23×C3⋊D75, D25×C3⋊D69, C3⋊D3×D575, … |
| maximal quotient of | C3⋊Dic1725, C2×C3⋊D1725 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 20);