Finite Group DatabasebetaFinite Group Databasebeta| order | 10350 |
| automorphism | Aut(G) order 13662000 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5175 |
| unambiguous semidirect product | C9⋊D575 |
| unambiguous semidirect product | C23⋊D225 |
| unambiguous semidirect product | C25⋊D207 |
| Fitting, derived, Hall | C9×C23×C25 ⋊ C2 |
| Hall | C23×C25 ⋊ D9 |
| Hall | C9×C25 ⋊ D23 |
| Hall | C9×C23 ⋊ D25 |
| Sylow | C25 ⋊ D207 |
| Sylow | C23 ⋊ D225 |
| Sylow | C9 ⋊ D575 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C9×C23×C25 | C2 |
| Frattini | C3×C5 | D345 |
| socle | C3×C5×C23 | D15 |
| LCS | G ▷ C9×C23×C25 | |
| UCS | C1 | |
36 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,23,3,5|b^3=e^2,c^5=f^4,b^a=b^2e,c^a=c^4f,d^a=d^22,e^a=e^2,f^a=f^42589 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D23×D225, D25×D207, D9×D575, … |
| maximal normal subgroup of | D23×D225, D25×D207, D9×D575, … |
| maximal quotient of | Dic5175, C2×D5175, D15525, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10350, 8);