Finite Group Databasebeta

← Group #305746

Character table — Group #305746

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-1-1-11111111111111111-1-1-1-1-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-11111-1-111-1
χ71111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-111-1-1-1111-1-1-1-111-1
χ81111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-11
χ91111111111111111-1-1-1-111111111-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11
χ101111111111111111-1-1-1-111111111-1-11111-1-11111-1-1-1-1111111-1-11-1-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111-1111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-11111111-1-11-1-1-1-1-1-1111
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1111-1-1-1111111-1-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-111111-1-111-1-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1-1-1-1-1-111-1-1-111-1-1111
χ172222222222-2-22-2-222222-2-2000000-2-200002222000000-2-2000000000-2000000000
χ182222222222-2-22-2-222222-2-2000000-2-20000-2-2-2-2000000220000000002000000000
χ192222222222-2-22-2-22-2-2-2-2-2-200000022000022-2-200000022000000000-2000000000
χ202222222222-2-22-2-22-2-2-2-2-2-2000000220000-2-222000000-2-20000000002000000000
χ2122222222-2-222-222-20000-2-22222220022-2-20000-2-2000000000000-2000000000000
χ2222222222-2-222-222-20000-2-22222-2-200-2-2220000-2-20000000000002000000000000
χ2322222222-2-222-222-20000-2-2-2-2-2-22200-2-222000022000000000000-2000000000000
χ2422222222-2-222-222-20000-2-2-2-2-2-2-2-20022-2-20000220000000000002000000000000
χ2522-22-2-2-222-200-200222-2-20022−2−2000000002i−2i2i−2i2−222−2−200i2i2−i2−i200000000i2−i200000
χ2622-22-2-2-222-200-200222-2-20022−2−200000000−2i2i−2i2i2−222−2−200−i2−i2i2i200000000−i2i200000
χ2722-22-2-2-222-200-200222-2-200−2−222000000002i−2i2i−2i−22−2−22200−i2−i2i2i200000000−i2i200000
χ2822-22-2-2-222-200-200222-2-200−2−22200000000−2i2i−2i2i−22−2−22200i2i2−i2−i200000000i2−i200000
χ2922-22-2-2-222-200-2002-2-2220022−2−2000000002i−2i−2i2i2−2−2−22200−i2−i2i2i200000000i2−i200000
χ3022-22-2-2-222-200-2002-2-2220022−2−200000000−2i2i2i−2i2−2−2−22200i2i2−i2−i200000000−i2i200000
χ3122-22-2-2-222-200-2002-2-22200−2−222000000002i−2i−2i2i−2222−2−200i2i2−i2−i200000000−i2i200000
χ3222-22-2-2-222-200-2002-2-22200−2−22200000000−2i2i2i−2i−2222−2−200−i2−i2i2i200000000i2−i200000
χ332-2-2222-2-22222-2-2-2-22-22-22-20000002-22-22-200000000000000002-20000000000000
χ342-2-2222-2-22222-2-2-2-22-22-22-20000002-2-22-220000000000000000-220000000000000
χ352-2-2222-2-22222-2-2-2-2-22-222-2000000-222-22-20000000000000000-220000000000000
χ362-2-2222-2-22222-2-2-2-2-22-222-2000000-22-22-2200000000000000002-20000000000000
χ372-2-2222-2-222-2-2-222-22-22-2-22000000-22000000000000000000000000002i−2i00002i−2i0
χ382-2-2222-2-222-2-2-222-22-22-2-22000000-2200000000000000000000000000−2i2i0000−2i2i0
χ392-2-2222-2-222-2-2-222-2-22-22-220000002-2000000000000000000000000002i−2i0000−2i2i0
χ402-2-2222-2-222-2-2-222-2-22-22-220000002-200000000000000000000000000−2i2i00002i−2i0
χ412-2-2222-2-2-2-2222-2-220000-22000000002-2-220000002i−2i2i−2i0000000002i−2i0000000000
χ422-2-2222-2-2-2-2222-2-220000-22000000002-2-22000000−2i2i−2i2i000000000−2i2i0000000000
χ432-2-2222-2-2-2-2222-2-220000-2200000000-222-20000002i−2i2i−2i000000000−2i2i0000000000
χ442-2-2222-2-2-2-2222-2-220000-2200000000-222-2000000−2i2i−2i2i0000000002i−2i0000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-44-4-4004-404-400000000000000000000000000000000000000000000022−22000
χ47444-4-44-4-4004-404-4000000000000000000000000000000000000000000000−2222000
χ48444-4-44-4-400-440-44000000000004-40000000000000000000000000000000000000
χ49444-4-44-4-400-440-4400000000000-440000000000000000000000000000000000000
χ5044-44-4-4-44-4400400-40000002222−22−22000000000000−22220000000000000000000000000
χ5144-44-4-4-44-4400400-4000000−22−22222200000000000022−220000000000000000000000000
χ524-444-4-44-44-400400-44-4-44000000000000000000000000000000000000000000000
χ534-444-4-44-44-400400-4-444-4000000000000000000000000000000000000000000000
χ544-444-4-44-4-4400-40040000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ554-444-4-44-4-4400-4004000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ564-44-44-4-440000000000000022−2222−220000000000000000002i2−2i22i−2i2i−2i000000000000000
χ574-44-44-4-440000000000000022−2222−22000000000000000000−2i22i2−2i2i−2i2i000000000000000
χ584-44-44-4-4400000000000000−2222−22220000000000000000002i2−2i2−2i2i−2i2i000000000000000
χ594-44-44-4-4400000000000000−2222−2222000000000000000000−2i22i22i−2i2i−2i000000000000000
χ604-4-4444-4-4-4-4-4-4444400004-40000000000000000000000000000000000000000000
χ614-4-4-4-4444004-40-44000000000000000000000000000000022−22−2222000000000000000
χ624-4-4-4-4444004-40-440000000000000000000000000000000−222222−22000000000000000
χ634-4-4-4-444400-4404-400000004-4-44000000000000000000000000000000000000000
χ644-4-4-4-444400-4404-40000000-444-4000000000000000000000000000000000000000
χ6588-8-88-88-8000000000000000000000000000000000000000000000000000000000

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