Finite Group DatabasebetaFinite Group Databasebeta| order | 7028 |
| automorphism | Aut(G) order 5271000 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3514 |
| direct product | C2×D1757 |
| unambiguous semidirect product | (C2×C7)⋊D251 |
| unambiguous semidirect product | (C2×C251)⋊D7 |
| Fitting, socle | C2×C7×C251 ⋊ C2 |
| derived, Hall | C7×C251 ⋊ C22 |
| Sylow | C251 ⋊ C2×D7 |
| Sylow | C7 ⋊ C2×D251 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1757 |
| commutator, hypocenter | C7×C251 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C7×C251 | C2 |
| LCS | G ▷ C7×C251 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
1760 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×ΓL(1,𝔽8)⋊D251, D3×D1757, C2×C3×D1757, … |
| maximal normal subgroup of | C2×ΓL(1,𝔽8)⋊D251, C2×C3×D1757, C2×C7⋊(D251⋊C5), … |
| maximal quotient of | D3×D1757, C2×C3×D1757, C2×D5271, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7028, 7);