Finite Group DatabasebetaFinite Group Databasebeta| order | 1050 |
| isoclinism | isoclinic class of D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C7 · Schur multiplier (H2) = C1 |
| direct product | C5×C7×D15 |
| unambiguous semidirect product | C3⋊(C5×C7×D5) |
| unambiguous semidirect product | C5⋊(C5×D3×C7) |
| Fitting, socle, Hall | C3×C52×C7 ⋊ C2 |
| derived | C3×C5 ⋊ C2×C5×C7 |
| Hall | C52×C7 ⋊ D3 |
| Hall | C3×C52 ⋊ C2×C7 |
| Sylow | C52 ⋊ D3×C7 |
| Hall | C3×C7 ⋊ C5×D5 |
| Sylow | C3 ⋊ C5×C7×D5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C7 | D15 |
| commutator, cosocle, hypocenter | C3×C5 | C2×C5×C7 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7 | C2 |
| LCS | G ▷ C3×C5 | |
| UCS | C1 ◁ C5×C7 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 210 |
315 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C5×D7×D15, C5×D3×C7×D5, C5×D15⋊D7, … |
| maximal normal subgroup of | C5×D7×D15, C5×D3×C7×D5, C5×D15⋊D7, … |
| maximal quotient of | C5×C7×Dic15, C2×C5×C7×D15, C5×C7×D45, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1050, 36);