Finite Group DatabasebetaFinite Group Databasebeta| order | 7028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D251 |
| unambiguous semidirect product | (D7×C251)⋊C2 |
| unambiguous semidirect product | (C7×D251)⋊C2 |
| unambiguous semidirect product | D1757⋊C2 |
| Fitting, socle, derived, Hall | C7×C251 ⋊ C22 |
| Sylow | C251 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D251 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C251 | C22 |
| LCS | G ▷ C7×C251 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
635 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×D251, C3×D7×D251, D21×D251, … |
| maximal normal subgroup of | AGL(1,𝔽7)×D251, C3×D7×D251, D7×D251⋊C5, … |
| maximal quotient of | C3×D7×D251, D21×D251, D7×D753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7028, 6);