Finite Group DatabasebetaFinite Group Databasebeta| order | 5684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | D7×D203 |
| unambiguous semidirect product | (C7×D7)⋊D29 |
| unambiguous semidirect product | (D7×C29)⋊D7 |
| Fitting, socle, derived, Hall | C72×C29 ⋊ C22 |
| Sylow | C72 ⋊ C2×D29 |
| Sylow | C29 ⋊ D72 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C29 | C22 |
| LCS | G ▷ C72×C29 | |
| UCS | C1 | |
52 conjugacy classes of subgroups.
515 conjugacy classes — view the full character table.
| maximal subgroup of | #64423⋊D29, #64422⋊D29, AGL(1,𝔽7)×D203, … |
| maximal normal subgroup of | #64423⋊D29, #64422⋊D29, AGL(1,𝔽7)×D203, … |
| maximal quotient of | C3×D7×D203, D7×D609, D21×D203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5684, 41);