Finite Group Databasebeta

← Group #304894

Character table — Group #304894

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888888888888844444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1111111
χ511111111111111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ611111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-1
χ711111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1111111-1-1
χ811111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-111-1-1-1-111
χ91111111111111111-1-1-1-111-111-111-1-1111111-1-1-1-11111-1-1-1-1-111-11-1-1-111-1-11-1
χ101111111111111111-1-1-1-111-111-111-1-111-1-1-1-11111-1-1-1-11111-111-11-1-1-1-1-111-11
χ111111111111111111-1-1-1-111-111-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-111-11
χ121111111111111111-1-1-1-111-111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-111111-1-11-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-111-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111-11111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-11-1-111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11111-11-1-1-1-1111-1
χ172222222222-2-222-2-22222-2-2-200-222220000000000000000000000-2-200000000
χ182222222222-2-222-2-22222-2-2-200-2-2-2-2-200000000000000000000002200000000
χ192222222222-2-222-2-2-2-2-2-2-2-2200222-2-20000000000000000000000-2200000000
χ202222222222-2-222-2-2-2-2-2-2-2-22002-2-22200000000000000000000002-200000000
χ2122222222-2-222-2-22222-2-2-2-2222-20000-2-20000000000000000-20020000000000
χ2222222222-2-222-2-22222-2-2-2-22-2-2-20000220000000000000000200-20000000000
χ2322222222-2-222-2-222-2-222-2-2-22220000-2-20000000000000000200-20000000000
χ2422222222-2-222-2-222-2-222-2-2-2-2-220000220000000000000000-20020000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-2002000000000000000000000002-20002-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-200200000000000000000000000-22000-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222200-2000000000000000000000002-2000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222200-200000000000000000000000-220002-2000000
χ29222-2-2-2-222-2-2-22-22200002-202-2000002-200002i2i−2i−2i00002i2i−2i−2i00000000000000
χ30222-2-2-2-222-2-2-22-22200002-202-2000002-20000−2i−2i2i2i0000−2i−2i2i2i00000000000000
χ31222-2-2-2-222-2-2-22-22200002-20-2200000-2200002i2i−2i−2i0000−2i−2i2i2i00000000000000
χ32222-2-2-2-222-2-2-22-22200002-20-2200000-220000−2i−2i2i2i00002i2i−2i−2i00000000000000
χ33222-2-2-2-22-22-2-2-22220000-2202-200000-222i2i−2i−2i00002i2i−2i−2i000000000000000000
χ34222-2-2-2-22-22-2-2-22220000-2202-200000-22−2i−2i2i2i0000−2i−2i2i2i000000000000000000
χ35222-2-2-2-22-22-2-2-22220000-220-22000002-22i2i−2i−2i0000−2i−2i2i2i000000000000000000
χ36222-2-2-2-22-22-2-2-22220000-220-22000002-2−2i−2i2i2i00002i2i−2i−2i000000000000000000
χ3722-2-22-22-2-2-20022002-22-20000002i−2i2i−2i0000000000i2−i2i2−i2i2−i2i2−i2000000002−22−200
χ3822-2-22-22-2-2-20022002-22-20000002i−2i2i−2i0000000000−i2i2−i2i2−i2i2−i2i200000000−22−2200
χ3922-2-22-22-2-2-20022002-22-2000000−2i2i−2i2i0000000000i2−i2i2−i2i2−i2i2−i200000000−22−2200
χ4022-2-22-22-2-2-20022002-22-2000000−2i2i−2i2i0000000000−i2i2−i2i2−i2i2−i2i2000000002−22−200
χ4122-2-22-22-2-2-2002200-22-220000002i−2i−2i2i0000000000i2−i2i2−i2−i2i2−i2i2000000002−2−2200
χ4222-2-22-22-2-2-2002200-22-220000002i−2i−2i2i0000000000−i2i2−i2i2i2−i2i2−i200000000−222−200
χ4322-2-22-22-2-2-2002200-22-22000000−2i2i2i−2i0000000000i2−i2i2−i2−i2i2−i2i200000000−222−200
χ4422-2-22-22-2-2-2002200-22-22000000−2i2i2i−2i0000000000−i2i2−i2i2i2−i2i2−i2000000002−2−2200
χ45444-4-4-4-444-4444-4-4-40000-440000000000000000000000000000000000000000
χ46444-4-4-4-44-4444-44-4-400004-40000000000000000000000000000000000000000
χ4744-44-44-4-44-400-440000000000000000000000000022−22−2222000000000000000000
χ4844-44-44-4-44-400-4400000000000000000000000000−222222−22000000000000000000
χ4944-44-44-4-4-44004-400000000000000000000000000000022−22−222200000000000000
χ5044-44-44-4-4-44004-4000000000000000000000000000000−222222−2200000000000000
χ5144-4-44-44-44400-4-4004-4-44000000000000000000000000000000000000000000
χ5244-4-44-44-44400-4-400-444-4000000000000000000000000000000000000000000
χ534-4444-4-4-4004-4004-40000000000000000000022−2222−220000000000000000000000
χ544-4444-4-4-4004-4004-400000000000000000000−2222−22220000000000000000000000
χ554-4444-4-4-400-4400-44000000000000000022−2222−2200000000000000000000000000
χ564-4444-4-4-400-4400-440000000000000000−2222−222200000000000000000000000000
χ574-44-4-444-4004-400-4400000000000000002i2−2i2−2i22i200000000000000000000000000
χ584-44-4-444-4004-400-440000000000000000−2i22i22i2−2i200000000000000000000000000
χ594-44-4-444-400-44004-4000000000000000000002i2−2i2−2i22i20000000000000000000000
χ604-44-4-444-400-44004-400000000000000000000−2i22i22i2−2i20000000000000000000000
χ618-8-88-8-888000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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