Finite Group DatabasebetaFinite Group Databasebeta| order | 1050 |
| isoclinism | isoclinic class of C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C5 |
| direct product | C2×C7×C52⋊C3 |
| unambiguous semidirect product | (C2×C52)⋊(C3×C7) |
| Fitting, socle, Hall | C2×C52×C7 ⋊ C3 |
| derived, Sylow | C52 ⋊ C2×C3×C7 |
| Hall | C52×C7 ⋊ C2×C3 |
| Hall | C2×C52 ⋊ C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | C52⋊C3 |
| commutator, cosocle, hypocenter | C52 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C52×C7 | C3 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C2×C7 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 210 |
154 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#64470, C7⋊#64470, Dic7×C52⋊C3, … |
| maximal normal subgroup of | C7×#64470, C7⋊#64470, Dic7×C52⋊C3, … |
| maximal quotient of | C4×C7×C52⋊C3, C22×C7×C52⋊C3, C2×C7×C52⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1050, 27);