Finite Group DatabasebetaFinite Group Databasebeta| order | 10710 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | C3⋊D1785 |
| unambiguous semidirect product | C5⋊(C3⋊D357) |
| unambiguous semidirect product | C7⋊(C3⋊D255) |
| unambiguous semidirect product | C17⋊(C3⋊D105) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C32×C5×C7×C17 | C2 |
| LCS | G ▷ C32×C5×C7×C17 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
Polycyclic presentation:
2,3^2,5,7,17|b^a=b^2,c^a=c^2,d^a=d^4,e^a=e^6,f^a=f^162679 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1785, D51×D105, D21×D255, … |
| maximal normal subgroup of | D3×D1785, D51×D105, D21×D255, … |
| maximal quotient of | C3⋊Dic1785, C2×C3⋊D1785 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10710, 42);