Finite Group DatabasebetaFinite Group Databasebeta| order | 6436 |
| automorphism | Aut(G) order 5174544 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3218 |
| direct product | C2×D1609 |
| unambiguous semidirect product | C1609⋊C22 |
| unambiguous semidirect product | (C2×C1609)⋊C2 |
| Fitting, socle | C2×C1609 ⋊ C2 |
| derived, Sylow | C1609 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D1609 |
| commutator, hypocenter | C1609 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1609 | C2 |
| LCS | G ▷ C1609 | |
| UCS | C1 ◁ C2 | |
10 conjugacy classes of subgroups.
1612 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D1609, C22⋊D1609, D6436, … |
| maximal normal subgroup of | C4×D1609, C22⋊D1609, D6436, … |
| maximal quotient of | C4×D1609, C2×Dic1609, C22⋊D1609, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6436, 4);