Finite Group DatabasebetaFinite Group Databasebeta| order | 10710 |
| automorphism | Aut(G) order 12337920 |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D5355 |
| unambiguous semidirect product | C5⋊D1071 |
| unambiguous semidirect product | C7⋊D765 |
| unambiguous semidirect product | C9⋊D595 |
| unambiguous semidirect product | C17⋊D315 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C5×C7×C9×C17 | C2 |
| Frattini | C3 | D1785 |
| socle | C3×C5×C7×C17 | D3 |
| LCS | G ▷ C5×C7×C9×C17 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,5,7,17,3|b^3=f^2,b^a=b^2f,c^a=c^4,d^a=d^6,e^a=e^16,f^a=f^22679 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D17×D315, D7×D765, D45×D119, … |
| maximal normal subgroup of | D17×D315, D7×D765, D45×D119, … |
| maximal quotient of | Dic5355, C2×D5355, D16065, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10710, 17);