Finite Group DatabasebetaFinite Group Databasebeta| order | 5644 |
| automorphism | Aut(G) order 3702464 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1411 |
| unambiguous semidirect product | C83⋊Dic17 |
| derived, Hall | C17×C83 ⋊ C4 |
| Sylow | C83 ⋊ Dic17 |
| Sylow | C17 ⋊ Dic83 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1411 |
| commutator, hypocenter | C17×C83 | C4 |
| Fitting, socle | C2×C17×C83 | C2 |
| LCS | G ▷ C17×C83 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,17,83,2|a^2=d,b^a=b^16,c^a=c^821414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1411, Dic4233, C5×Dic1411, … |
| maximal normal subgroup of | C3×Dic1411, C5×Dic1411, Dic2822 |
| maximal quotient of | C3×Dic1411, Dic4233, C5×Dic1411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5644, 4);