Finite Group DatabasebetaFinite Group Databasebeta| order | 5684 |
| automorphism | Aut(G) order 3342192 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2842 |
| direct product | C2×D1421 |
| unambiguous semidirect product | (C2×C29)⋊D49 |
| unambiguous semidirect product | (C2×C49)⋊D29 |
| Fitting | C2×C29×C49 ⋊ C2 |
| derived, Hall | C29×C49 ⋊ C22 |
| Sylow | C49 ⋊ C2×D29 |
| Sylow | C29 ⋊ C2×D49 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1421 |
| commutator, hypocenter | C29×C49 | C22 |
| Frattini | C7 | C2×D203 |
| Fitting | C2×C29×C49 | C2 |
| socle | C2×C7×C29 | D7 |
| LCS | G ▷ C29×C49 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
1424 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C29⋊(D49⋊C3), D3×D1421, C2×C3×D1421, … |
| maximal normal subgroup of | C2×C29⋊(D49⋊C3), C2×C3×D1421, C2×C5×D1421, … |
| maximal quotient of | D3×D1421, C2×C3×D1421, C2×D4263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5684, 16);