Finite Group DatabasebetaFinite Group Databasebeta| order | 1050 |
| isoclinism | isoclinic class of #3874 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C7 · Schur multiplier (H2) = C1 |
| direct product | C7×#3874 |
| Fitting, socle, Hall | C52×C7 ⋊ D3 |
| derived, Hall | C52⋊C3 ⋊ C2×C7 |
| Hall | C7×C52⋊C3 ⋊ C2 |
| Sylow | C52 ⋊ D3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #3874 |
| commutator, cosocle, hypocenter | C52⋊C3 | C2×C7 |
| Frattini | C1 | G |
| Fitting, socle | C52×C7 | D3 |
| LCS | G ▷ C52⋊C3 | |
| UCS | C1 ◁ C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 105 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#3874⋊C2, #3874⋊D7, D7×#3874, … |
| maximal normal subgroup of | C7×#3874⋊C2, #3874⋊D7, D7×#3874, … |
| maximal quotient of | C7×#64470, C2×C7×#3874, C7×#90646, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1050, 13);