Finite Group DatabasebetaFinite Group Databasebeta| order | 5628 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| direct product | D7×D67⋊C3 |
| unambiguous semidirect product | D67⋊(C3×D7) |
| unambiguous semidirect product | (C7×D67⋊C3)⋊C2 |
| unambiguous semidirect product | (D7×C67⋊C3)⋊C2 |
| unambiguous semidirect product | ((C67⋊C3)⋊D7)⋊C2 |
| Fitting, socle, derived, Hall | C7×C67 ⋊ C22×C3 |
| Hall | D7×D67 ⋊ C3 |
| Hall | C7×C67⋊C3 ⋊ C22 |
| Hall | C67⋊C3 ⋊ C2×D7 |
| Sylow | C67 ⋊ C2×C3×D7 |
| Sylow | C7 ⋊ C2×D67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C7×C67 | C22×C3 |
| LCS | G ▷ C7×C67 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
85 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽7)×D67⋊C3, C3×D7×D67⋊C3, D21×D67⋊C3, … |
| maximal normal subgroup of | AGL(1,𝔽7)×D67⋊C3, C3×D7×D67⋊C3, C5×D7×D67⋊C3 |
| maximal quotient of | D7×D67⋊C9, C3×D7×D67⋊C3, D21×D67⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5628, 29);