Finite Group Databasebeta

← Group #176809

Character table — Group #176809

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size111111114444444444888888888816161616161616161616161616161616161616163232
order12222222444444444444444444444444444488888888888822
χ111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-11-1-1-11-111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111-1-111-1-111111-1-11-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111111111-1-111-1-111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111-1-111-1-1-1-1-1-1-11-1-111-111111-1-1-1-1-1-1-1-111
χ8111111111111111111-1-111-1-1-1-1-1-1-11-1-111-11-1-1-1-111111111-1-1
χ911111111-1-1-1-111111111-1-1-1-111-1-1-1111-1-1-1111-1-111-1-111-1-11-1
χ1011111111-1-1-1-111111111-1-1-1-111-1-1-1111-1-1-11-1-111-1-111-1-111-11
χ1111111111-1-1-1-111111111-1-1-1-1-1-1111-11-111-1-111-1-111-1-1-1-111-11
χ1211111111-1-1-1-111111111-1-1-1-1-1-1111-11-111-1-1-1-111-1-11111-1-11-1
χ1311111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11111-111-1-1-1-11111-1-1-11
χ1411111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-11111-1-1-11111-1-1-1-1111-1
χ1511111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111-1-1111-1
χ1611111111-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-111-1-11111-1-111-1-1-11
χ172222222222222-2-2-22-222-2-222000000-2000-2000000000000000
χ182222222222222-2-2-22-2-2-2-2-2-2-200000020002000000000000000
χ192222222222-2-2-22-2-2-22002-2002222-200-2000000000000000000
χ202222222222-2-2-22-2-2-22002-200-2-2-2-22002000000000000000000
χ212222222222-2-2-2-222-2-200-2200000002002-20-200000000000000
χ222222222222-2-2-2-222-2-200-220000000-200-220200000000000000
χ2322222222-2-222-22-2-2-2200-220022-2-2200-2000000000000000000
χ2422222222-2-222-22-2-2-2200-2200-2-222-2002000000000000000000
χ2522222222-2-222-2-222-2-2002-20000000200-220-200000000000000
χ2622222222-2-222-2-222-2-2002-20000000-2002-20200000000000000
χ2722222222-2-2-2-22-2-2-22-22222-2-2000000-20002000000000000000
χ2822222222-2-2-2-22-2-2-22-2-2-222220000002000-2000000000000000
χ29444-44-4-4-4004-4000000000000000000000000000000002i−2i2i−2i00
χ30444-44-4-4-4004-400000000000000000000000000000000−2i2i−2i2i00
χ31444-44-4-4-400-44000000000000000000000000000000002i−2i−2i2i00
χ32444-44-4-4-400-4400000000000000000000000000000000−2i2i2i−2i00
χ3344-44-44-4-40000004-4000000000000000000000000002i2−2i2000000
χ3444-44-44-4-40000004-400000000000000000000000000−2i22i2000000
χ3544-44-44-4-4000000-440000000000000000000000002i2−2i200000000
χ3644-44-44-4-4000000-44000000000000000000000000−2i22i200000000
χ3744-4-4-4-444000004000-40000004i−4i000000000000000000000000
χ3844-4-4-4-444000004000-4000000−4i4i000000000000000000000000
χ3944-4-4-4-44400000-40004000000004-40000000000000000000000
χ4044-4-4-4-44400000-4000400000000-440000000000000000000000
χ414-444-4-44-44-4000000000000000000000000002i−2i2i−2i0000000000
χ424-444-4-44-44-400000000000000000000000000−2i2i−2i2i0000000000
χ434-444-4-44-4-44000000000000000000000000002i−2i−2i2i0000000000
χ444-444-4-44-4-4400000000000000000000000000−2i2i2i−2i0000000000
χ454-4-4-4444-400004000-404i−4i000000000000000000000000000000
χ464-4-4-4444-400004000-40−4i4i000000000000000000000000000000
χ474-4-4-4444-40000-40004000004-400000000000000000000000000
χ484-4-4-4444-40000-4000400000-4400000000000000000000000000
χ498-88-8-88-88000000000000000000000000000000000000000000
χ508-8-888-8-88000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).