Finite Group DatabasebetaFinite Group Databasebeta| order | 5756 |
| automorphism | Aut(G) order 4138564 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1439 |
| unambiguous semidirect product | C1439⋊C4 |
| derived, Sylow | C1439 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1439 |
| commutator, hypocenter | C1439 | C4 |
| Fitting, socle | C2×C1439 | C2 |
| LCS | G ▷ C1439 | |
| UCS | C1 ◁ C2 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,1439|a^2=b,c^a=c^14381442 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D1439, C2×Dic1439, C22⋊D1439, … |
| maximal normal subgroup of | C4×D1439, C2×Dic1439, C22⋊D1439, … |
| maximal quotient of | C1439⋊C8, C2×Dic1439, C3×Dic1439, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5756, 1);