Finite Group DatabasebetaFinite Group Databasebeta| order | 7028 |
| isoclinism | isoclinic class of D251 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C2×C7×D251 |
| unambiguous semidirect product | C251⋊(C22×C7) |
| unambiguous semidirect product | (C2×C251)⋊(C2×C7) |
| Fitting, socle | C2×C7×C251 ⋊ C2 |
| derived, Sylow | C251 ⋊ C22×C7 |
| Hall | C7×C251 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C7 | D251 |
| commutator, hypocenter | C251 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C251 | C2 |
| LCS | G ▷ C251 | |
| UCS | C1 ◁ C2×C7 | |
20 conjugacy classes of subgroups.
1778 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×ΓL(1,𝔽8)×D251, D3×C7×D251, C2×C3×C7×D251, … |
| maximal normal subgroup of | C2×ΓL(1,𝔽8)×D251, C2×C3×C7×D251, C2×C7×D251⋊C5, … |
| maximal quotient of | D3×C7×D251, C2×C3×C7×D251, C2×C7×D753, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7028, 9);