Finite Group DatabasebetaFinite Group Databasebeta| order | 10710 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C3×D1785 |
| unambiguous semidirect product | C3⋊(C3×D595) |
| unambiguous semidirect product | C5⋊(C3×D357) |
| unambiguous semidirect product | C17⋊(C3×D105) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D1785 |
| commutator, cosocle, hypocenter | C3×C5×C7×C17 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C17 | C2 |
| LCS | G ▷ C3×C5×C7×C17 | |
| UCS | C1 ◁ C3 | |
72 conjugacy classes of subgroups.
2682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×D17×D105, C3×D7×D255, C3×D15×D119, … |
| maximal normal subgroup of | C3×D17×D105, C3×D7×D255, C3×D15×D119, … |
| maximal quotient of | C3×Dic1785, C2×C3×D1785 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10710, 50);