Finite Group Databasebeta

← Group #349592

Character table — Group #349592

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244448888888888888888888888888888888888816161616161616163232
order12222222444444444444224444444444444444444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1111-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-11-1-111111-1-1-1-1-1-111-1-1-1-11-1-11111111111-1-1-1-11111-1-1
χ611111111111111111111-1-11-1-111111-1-1-1-1-1-111-1-1-1-11-1-111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-11-1-1-1-1-1-111111-1-1-1-111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-11-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111111111111-1-1111-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-11-1
χ1011111111111111111-1-1111-1-1-111-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-11
χ1111111111111111111-1-1111-1-1-1-1-111-1-1-1-1-111111111-1-1-1-1-11111-1-1-1-111-1-1-1-111-11
χ1211111111111111111-1-1111-1-1-1-1-111-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-1-11111-1-11-1
χ1311111111111111111-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1-1-1-1-11111-1-1-11
χ1411111111111111111-1-11-1-1-11111-1-1-1-1-1-1-1-1-1-1-11111-11111-1-1-1-1111111-1-1-1-1111-1
χ1511111111111111111-1-11-1-1-111-1-111-11111-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1111-1
χ1611111111111111111-1-11-1-1-111-1-111-11111-1-111-1-1-1-1-111-1-1-1-1-1-1111111-1-111-1-1-11
χ172222222222-2-222-2-2-222-222-2220000-20000-2-20000002-2-200000000000000000000
χ182222222222-2-222-2-2-222-2-2-2-2-2-20000-200002200000022200000000000000000000
χ192222222222-2-222-2-2-2-2-2-2222-2-2000020000-2-2000000-22200000000000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-222200002000022000000-2-2-200000000000000000000
χ2122222222-2-222-2-222-222-200-20022222000000-2-20000-200-2-2000000000000000000
χ2222222222-2-222-2-222-222-200-200-2-2-2-22000000220000-20022000000000000000000
χ2322222222-2-222-2-222-2-2-2-20020022-2-2-2000000220000200-2-2000000000000000000
χ2422222222-2-222-2-222-2-2-2-200200-2-222-2000000-2-2000020022000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222002000000-222-2-2000022-2-2-20000000000000000000000
χ2622222222-2-2-2-2-2-2-2-22222002000000-2-2-2220000-2-222-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-22-2-2200-2000000222-2-20000-2-22220000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22-2-2200-20000002-2-222000022-2-220000000000000000000000
χ29222-2-2-22-22222-2-2-2-2200-22-2000002-2000002-22-22-22-200000000000000000000000
χ30222-2-2-22-22222-2-2-2-2200-22-200000-22000002-2-22-22-2200000000000000000000000
χ31222-2-2-22-22222-2-2-2-2200-2-22000002-200000-222-2-22-2200000000000000000000000
χ32222-2-2-22-22222-2-2-2-2200-2-2200000-2200000-22-222-22-200000000000000000000000
χ33222-2-2-22-222-2-2-2-222-20022-20002i−2i0002i−2i2i−2i-220000000002i−2i000000000000000000
χ34222-2-2-22-222-2-2-2-222-20022-2000−2i2i000−2i2i−2i2i-22000000000−2i2i000000000000000000
χ35222-2-2-22-222-2-2-2-222-2002-220002i−2i000−2i2i−2i2i2-20000000002i−2i000000000000000000
χ36222-2-2-22-222-2-2-2-222-2002-22000−2i2i0002i−2i2i−2i2-2000000000−2i2i000000000000000000
χ37222-2-2-22-2-2-22222-2-2-20020002i−2i002-202i−2i−2i2i00-22000002i−2i00000000000000000000
χ38222-2-2-22-2-2-22222-2-2-20020002i−2i00-220−2i2i2i−2i002-2000002i−2i00000000000000000000
χ39222-2-2-22-2-2-22222-2-2-2002000−2i2i002-20−2i2i2i−2i00-2200000−2i2i00000000000000000000
χ40222-2-2-22-2-2-22222-2-2-2002000−2i2i00-2202i−2i−2i2i002-200000−2i2i00000000000000000000
χ41222-2-2-22-2-2-2-2-22222200-20002i−2i2i−2i000000000002-2-220−2i2i−2i2i000000000000000000
χ42222-2-2-22-2-2-2-2-22222200-20002i−2i−2i2i00000000000-222-20−2i2i2i−2i000000000000000000
χ43222-2-2-22-2-2-2-2-22222200-2000−2i2i2i−2i00000000000-222-202i−2i−2i2i000000000000000000
χ44222-2-2-22-2-2-2-2-22222200-2000−2i2i−2i2i000000000002-2-2202i−2i2i−2i000000000000000000
χ4544-44-44-4-44-4004-4000000000000000000000000000000000000000000022−22000000
χ4644-44-44-4-44-4004-40000000000000000000000000000000000000000000−2222000000
χ4744-44-44-4-4-4400-440000000000000000000000000000000000000000022−2200000000
χ4844-44-44-4-4-4400-4400000000000000000000000000000000000000000−222200000000
χ4944-4-44-4-444-400-4400000000000000000000000000000000000002i22i2−2i2−2i20000000000
χ5044-4-44-4-444-400-440000000000000000000000000000000000000−2i2−2i22i22i20000000000
χ5144-4-44-4-44-44004-40000000000000000000000000000000002i22i2−2i2−2i200000000000000
χ5244-4-44-4-44-44004-4000000000000000000000000000000000−2i2−2i22i22i200000000000000
χ534-4444-4-4-40000000004-400000000000000000000000000002-22-22-22-20000000000
χ544-4444-4-4-40000000004-40000000000000000000000000000-22-22-22-220000000000
χ554-4444-4-4-4000000000-4400000000000000000000000000002-22-2-22-220000000000
χ564-4444-4-4-4000000000-440000000000000000000000000000-22-222-22-20000000000
χ574-4-44-4-444004-4004-400000000000000000000000000000000000000000000022−2200
χ584-4-44-4-444004-4004-4000000000000000000000000000000000000000000000−222200
χ594-4-44-4-44400-4400-44000000000000000000000000000000000000000000022−220000
χ604-4-44-4-44400-4400-440000000000000000000000000000000000000000000−22220000
χ614-4-4-4444-4004-400-4400000000000000000000000000000002i2−2i2−2i22i200000000000000
χ624-4-4-4444-4004-400-440000000000000000000000000000000−2i22i22i2−2i200000000000000
χ634-4-4-4444-400-44004-4000000000000000000000000000000000002i2−2i2−2i22i20000000000
χ644-4-4-4444-400-44004-400000000000000000000000000000000000−2i22i22i2−2i20000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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