Finite Group DatabasebetaFinite Group Databasebeta| order | 1050 |
| isoclinism | isoclinic class of D7×C52⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
| direct product | D7×C52⋊C3 |
| Fitting, socle, derived, Hall | C52×C7 ⋊ C2×C3 |
| Hall | C7×C52⋊C3 ⋊ C2 |
| Hall | C52×D7 ⋊ C3 |
| Sylow | C52 ⋊ C3×D7 |
| Sylow | C7 ⋊ C2×C52⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C7 | C2×C3 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 105 |
55 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#3874, D7×(C5⋊D5)⋊C3, C2×D7×C52⋊C3, … |
| maximal normal subgroup of | D7×#3874, D7×(C5⋊D5)⋊C3, C2×D7×C52⋊C3, … |
| maximal quotient of | Dic7×C52⋊C3, C2×D7×C52⋊C3, D7×C52⋊C9, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1050, 20);