Finite Group DatabasebetaFinite Group Databasebeta| order | 5684 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C7 |
| direct product | D29×C7⋊D7 |
| unambiguous semidirect product | (C7×D29)⋊D7 |
| Fitting, socle, derived, Hall | C72×C29 ⋊ C22 |
| Sylow | C72 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×C7⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C72×C29 | C22 |
| LCS | G ▷ C72×C29 | |
| UCS | C1 | |
100 conjugacy classes of subgroups.
416 conjugacy classes — view the full character table.
| maximal subgroup of | D29×#64424, D29×#64425, D29×ΓL(1,𝔽8)⋊D7, … |
| maximal normal subgroup of | D29×#64424, D29×#64425, D29×ΓL(1,𝔽8)⋊D7, … |
| maximal quotient of | C3×D29×C7⋊D7, D29×C3⋊(C7⋊D7), C7⋊D7×D87, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5684, 39);