Finite Group DatabasebetaFinite Group Databasebeta| order | 6404 |
| automorphism | Aut(G) order 5123200 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3202 |
| direct product | C2×D1601 |
| unambiguous semidirect product | C1601⋊C22 |
| unambiguous semidirect product | (C2×C1601)⋊C2 |
| Fitting, socle | C2×C1601 ⋊ C2 |
| derived, Sylow | C1601 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1601 |
| commutator, hypocenter | C1601 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1601 | C2 |
| LCS | G ▷ C1601 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
1604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D1601, C22⋊D1601, D6404, … |
| maximal normal subgroup of | C4×D1601, C22⋊D1601, D6404, … |
| maximal quotient of | C4×D1601, C2×Dic1601, C22⋊D1601, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6404, 4);