Finite Group Databasebeta

← Group #309944

Character table — Group #309944

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1111-111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-11-1-1-1-111-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1-1111-1-111-1-111-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-1-1-111-1-1111
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11-1-1111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-111111111-1-1-1
χ91111111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-11
χ101111111111111111-1-1-1-1111111-1-1111111-1-1111111-1-1-1-111111-1-1-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-11111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111-1-1-111111-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111-1-1-11111-1-111-1
χ17222222222-2-222-2-222222-2-20000-2-2000000220022-2-200000000000-200000000000
χ18222222222-2-222-2-222222-2-20000-2-2000000-2-200-2-22200000000000200000000000
χ19222222222-2-222-2-22-2-2-2-2-2-20000220000002200-2-22200000000000-200000000000
χ20222222222-2-222-2-22-2-2-2-2-2-2000022000000-2-20022-2-200000000000200000000000
χ2122222222-222-2-222-20000-2-222220022-2-22200-2-2000000000000-200000000000000
χ2222222222-222-2-222-20000-2-2222200-2-222-2-200-2-2000000000000200000000000000
χ2322222222-222-2-222-20000-2-2-2-2-2-20022-2-2-2-20022000000000000200000000000000
χ2422222222-222-2-222-20000-2-2-2-2-2-200-2-222220022000000000000-200000000000000
χ2522-2-2-2-2222002-200-22i2i−2i−2i0022−2−2000000002i−2i2−22-200i2i2−i2−i222−2−200000000i2−i200000
χ2622-2-2-2-2222002-200-22i2i−2i−2i0022−2−200000000−2i2i2−2-2200i2i2−i2−i2−2−22200000000−i2i200000
χ2722-2-2-2-2222002-200-22i2i−2i−2i00−2−222000000002i−2i−222-200−i2−i2i2i2−2−22200000000−i2i200000
χ2822-2-2-2-2222002-200-22i2i−2i−2i00−2−22200000000−2i2i−22-2200−i2−i2i2i222−2−200000000i2−i200000
χ2922-2-2-2-2222002-200-2−2i−2i2i2i0022−2−2000000002i−2i2−2-2200−i2−i2i2i2−2−22200000000i2−i200000
χ3022-2-2-2-2222002-200-2−2i−2i2i2i0022−2−200000000−2i2i2−22-200−i2−i2i2i222−2−200000000−i2i200000
χ3122-2-2-2-2222002-200-2−2i−2i2i2i00−2−222000000002i−2i−22-2200i2i2−i2−i222−2−200000000−i2i200000
χ3222-2-2-2-2222002-200-2−2i−2i2i2i00−2−22200000000−2i2i−222-200i2i2−i2−i2−2−22200000000i2−i200000
χ332-2-22-222-2222-2-2-2-222i−2i2i−2i-2200002i−2i00000000000000000000000000002i−2i002-2000
χ342-2-22-222-2222-2-2-2-222i−2i2i−2i-2200002i−2i0000000000000000000000000000−2i2i00-22000
χ352-2-22-222-2222-2-2-2-22−2i2i−2i2i-220000−2i2i00000000000000000000000000002i−2i00-22000
χ362-2-22-222-2222-2-2-2-22−2i2i−2i2i-220000−2i2i0000000000000000000000000000−2i2i002-2000
χ372-2-22-222-22-2-2-2-22222i−2i2i−2i2-20000−2i2i2i−2i2i−2i00000000000000000002-2000000000000
χ382-2-22-222-22-2-2-2-22222i−2i2i−2i2-20000−2i2i−2i2i−2i2i0000000000000000000-22000000000000
χ392-2-22-222-22-2-2-2-2222−2i2i−2i2i2-200002i−2i2i−2i2i−2i0000000000000000000-22000000000000
χ402-2-22-222-22-2-2-2-2222−2i2i−2i2i2-200002i−2i−2i2i−2i2i00000000000000000002-2000000000000
χ412-2-22-222-2-2-2-22222-20000-220000002i−2i−2i2i00000000002-22-2000000002i−2i000000000
χ422-2-22-222-2-2-2-22222-20000-220000002i−2i−2i2i0000000000-22-2200000000−2i2i000000000
χ432-2-22-222-2-2-2-22222-20000-22000000−2i2i2i−2i00000000002-22-200000000−2i2i000000000
χ442-2-22-222-2-2-2-22222-20000-22000000−2i2i2i−2i0000000000-22-22000000002i−2i000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-44-4-40000000000000022−2222−220000000000000022−2200002-22-2000000000000000
χ47444-4-44-4-40000000000000022−2222−2200000000000000−22220000-22-22000000000000000
χ48444-4-44-4-400000000000000−2222−22220000000000000022−220000-22-22000000000000000
χ49444-4-44-4-400000000000000−2222−222200000000000000−222200002-22-2000000000000000
χ5044-444-4-4-404-4004-4000000000000000000000000000000022−22−2222000000000000000
χ5144-444-4-4-404-4004-40000000000000000000000000000000−222222−22000000000000000
χ5244-444-4-4-40-4400-4400000004-4-44000000000000000000000000000000000000000
χ5344-444-4-4-40-4400-440000000-444-4000000000000000000000000000000000000000
χ5444-4-4-4-444-400-440040000002222−22−220000000000−2222000000000000000000000000000
χ5544-4-4-4-444-400-44004000000−22−222222000000000022−22000000000000000000000000000
χ564-444-4-4-4404-400-44000000000000000004i−4i0000000000000000000000000000000
χ574-444-4-4-4404-400-4400000000000000000−4i4i0000000000000000000000000000000
χ584-444-4-4-440-44004-4000000000000000000000000000000000000000000000002i2−2i20
χ594-444-4-4-440-44004-400000000000000000000000000000000000000000000000−2i22i20
χ604-44-44-44-4400-4400-44-4-44000000000000000000000000000000000000000000000
χ614-44-44-44-4400-4400-4-444-4000000000000000000000000000000000000000000000
χ624-44-44-44-4-4004-4004000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ634-44-44-44-4-4004-400400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ644-4-44-444-4-44444-4-4-400004-40000000000000000000000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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