Finite Group DatabasebetaFinite Group Databasebeta| order | 1050 |
| isoclinism | isoclinic class of D21 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C52 · Schur multiplier (H2) = C5 |
| direct product | C52×D21 |
| unambiguous semidirect product | C3⋊(C52×D7) |
| unambiguous semidirect product | C7⋊(C52×D3) |
| Fitting, socle, Hall | C3×C52×C7 ⋊ C2 |
| derived, Hall | C3×C7 ⋊ C2×C52 |
| Hall | C52×C7 ⋊ D3 |
| Hall | C3×C52 ⋊ D7 |
| Sylow | C7 ⋊ C52×D3 |
| Sylow | C3 ⋊ C52×D7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C52 | D21 |
| commutator, cosocle, hypocenter | C3×C7 | C2×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7 | C2 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C52 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 525 |
300 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52×D3×D7, C5×D5×D21, C5×D15⋊D7, … |
| maximal normal subgroup of | C52×D3×D7, C5×D5×D21, C5×D15⋊D7, … |
| maximal quotient of | C52×Dic21, C2×C52×D21, C52×D63, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1050, 35);