Finite Group DatabasebetaFinite Group Databasebeta| order | 10710 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7×C17 · Schur multiplier (H2) = C1 |
| direct product | C3×C7×C17×D15 |
| unambiguous semidirect product | C3⋊(C3×C7×D5×C17) |
| unambiguous semidirect product | C5⋊(C3×D3×C7×C17) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C7×C17 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C2×C3×C7×C17 |
| Frattini | C1 | G |
| Fitting, socle | C32×C5×C7×C17 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C3×C7×C17 | |
72 conjugacy classes of subgroups.
3213 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C7×D15×D17, C3×D7×C17×D15, C3×D15×D119, … |
| maximal normal subgroup of | C3×C7×D15×D17, C3×D7×C17×D15, C3×D15×D119, … |
| maximal quotient of | C3×C7×C17×Dic15, C2×C3×C7×C17×D15 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10710, 53);