Finite Group DatabasebetaFinite Group Databasebeta| order | 7036 |
| automorphism | Aut(G) order 6184644 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1759 |
| unambiguous semidirect product | C1759⋊C4 |
| derived, Sylow | C1759 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1759 |
| commutator, hypocenter | C1759 | C4 |
| Fitting, socle | C2×C1759 | C2 |
| LCS | G ▷ C1759 | |
| UCS | C1 ◁ C2 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,1759|a^2=b,c^a=c^17581762 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D1759, C2×Dic1759, C22⋊D1759, … |
| maximal normal subgroup of | C4×D1759, C2×Dic1759, C22⋊D1759, … |
| maximal quotient of | C1759⋊C8, C2×Dic1759, C3×Dic1759, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7036, 1);