Finite Group DatabasebetaFinite Group Databasebeta| order | 5684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C29 · Schur multiplier (H2) = C2 |
| direct product | D72×C29 |
| unambiguous semidirect product | (C7×D7)⋊(C2×C29) |
| unambiguous semidirect product | (C7⋊D7)⋊(C2×C29) |
| Fitting, socle, Hall | C72×C29 ⋊ C22 |
| derived, Sylow | C72 ⋊ C22×C29 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C29 | D72 |
| commutator, hypocenter | C72 | C22×C29 |
| Frattini | C1 | G |
| Fitting, socle | C72×C29 | C22 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C29 | |
52 conjugacy classes of subgroups.
725 conjugacy classes — view the full character table.
| maximal subgroup of | C29×#64423⋊C2, C29×#64422⋊C2, D7×C29×AGL(1,𝔽7), … |
| maximal normal subgroup of | C29×#64423⋊C2, C29×#64422⋊C2, D7×C29×AGL(1,𝔽7), … |
| maximal quotient of | C3×D72×C29, D7×C29×D21, C29×D21⋊D7, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5684, 40);