Finite Group DatabasebetaFinite Group Databasebeta| order | 5644 |
| automorphism | Aut(G) order 3702464 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D2822 |
| direct product | C2×D1411 |
| unambiguous semidirect product | (C2×C17)⋊D83 |
| unambiguous semidirect product | (C2×C83)⋊D17 |
| Fitting, socle | C2×C17×C83 ⋊ C2 |
| derived, Hall | C17×C83 ⋊ C22 |
| Sylow | C83 ⋊ C2×D17 |
| Sylow | C17 ⋊ C2×D83 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1411 |
| commutator, hypocenter | C17×C83 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C17×C83 | C2 |
| LCS | G ▷ C17×C83 | |
| UCS | C1 ◁ C2 | |
20 conjugacy classes of subgroups.
1414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D3×D1411, C2×D4233, C2×C3×D1411, … |
| maximal normal subgroup of | C2×C3×D1411, C2×C5×D1411, D5644 |
| maximal quotient of | D3×D1411, C2×D4233, C2×C3×D1411, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5644, 9);