Finite Group Databasebeta

← Group #309924

Character table — Group #309924

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-111-1111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1111111111111111111-1-11-1-1-1-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-1-1
χ61111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1111
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111
χ81111111111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1111111111-1-1-1
χ91111111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11
χ101111111111111111-1-1-1-1111111111111-1-1-1-1111111-1-1-1-11111-1-1-11-1-1-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-11111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111111-1-11-11111-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-111-11-1-11111-1-111-1
χ1722222222222-2-2-2-222222-2-2000000000022-2-20022-2-20000000000-2000000000000
χ1822222222222-2-2-2-222222-2-20000000000-2-2-2-200-2-22200000000002000000000000
χ1922222222222-2-2-2-22-2-2-2-2-2-20000000000222200-2-2220000000000-2000000000000
χ2022222222222-2-2-2-22-2-2-2-2-2-20000000000-2-2220022-2-200000000002000000000000
χ2122222222-2-2-22222-20000-2-2222222-2-2-2-20000-2-2000000000000000200000000000
χ2222222222-2-2-22222-20000-2-22222-2-222220000-2-2000000000000000-200000000000
χ2322222222-2-2-22222-20000-2-2-2-2-2-22222-2-2000022000000000000000-200000000000
χ2422222222-2-2-22222-20000-2-2-2-2-2-2-2-2-2-222000022000000000000000200000000000
χ2522-22-2-2-2222-20000-22i2i−2i−2i0022−2−20000002i−2i002−22-200i2i2−i2−i222−2−200000000i2−i200000
χ2622-22-2-2-2222-20000-22i2i−2i−2i0022−2−2000000−2i2i002−2-2200i2i2−i2−i2−2−22200000000−i2i200000
χ2722-22-2-2-2222-20000-22i2i−2i−2i00−2−2220000002i−2i00−222-200−i2−i2i2i2−2−22200000000−i2i200000
χ2822-22-2-2-2222-20000-22i2i−2i−2i00−2−222000000−2i2i00−22-2200−i2−i2i2i222−2−200000000i2−i200000
χ2922-22-2-2-2222-20000-2−2i−2i2i2i0022−2−20000002i−2i002−2-2200−i2−i2i2i2−2−22200000000i2−i200000
χ3022-22-2-2-2222-20000-2−2i−2i2i2i0022−2−2000000−2i2i002−22-200−i2−i2i2i222−2−200000000−i2i200000
χ3122-22-2-2-2222-20000-2−2i−2i2i2i00−2−2220000002i−2i00−22-2200i2i2−i2−i222−2−200000000−i2i200000
χ3222-22-2-2-2222-20000-2−2i−2i2i2i00−2−222000000−2i2i00−222-200i2i2−i2−i2−2−22200000000i2−i200000
χ332-2-222-22-22-2-222-2-222i−2i2i−2i-220000000000002i−2i000000000000000000002i−2i002-2000
χ342-2-222-22-22-2-222-2-222i−2i2i−2i-220000000000002i−2i00000000000000000000−2i2i00-22000
χ352-2-222-22-22-2-222-2-22−2i2i−2i2i-22000000000000−2i2i000000000000000000002i−2i00-22000
χ362-2-222-22-22-2-222-2-22−2i2i−2i2i-22000000000000−2i2i00000000000000000000−2i2i002-2000
χ372-2-222-22-22-2-2-2-22222i−2i2i−2i2-200002i−2i002i−2i00−2i2i000000000000002-20000000000000
χ382-2-222-22-22-2-2-2-22222i−2i2i−2i2-20000−2i2i00−2i2i00−2i2i00000000000000-220000000000000
χ392-2-222-22-22-2-2-2-2222−2i2i−2i2i2-200002i−2i002i−2i002i−2i00000000000000-220000000000000
χ402-2-222-22-22-2-2-2-2222−2i2i−2i2i2-20000−2i2i00−2i2i002i−2i000000000000002-20000000000000
χ412-2-222-22-2-222-2-222-20000-2200002i−2i00−2i2i00000000002-22-2000000002i−2i000000000
χ422-2-222-22-2-222-2-222-20000-2200002i−2i00−2i2i0000000000-22-2200000000−2i2i000000000
χ432-2-222-22-2-222-2-222-20000-220000−2i2i002i−2i00000000002-22-200000000−2i2i000000000
χ442-2-222-22-2-222-2-222-20000-220000−2i2i002i−2i0000000000-22-22000000002i−2i000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-44-4-4-40004-44-40000000000000000000000000000000000000000000000022−220
χ47444-44-4-4-40004-44-400000000000000000000000000000000000000000000000−22220
χ48444-44-4-4-4000-44-4400000000000004-400000000000000000000000000000000000
χ49444-44-4-4-4000-44-440000000000000-4400000000000000000000000000000000000
χ5044-44-4-4-44-4-44000040000002222−22−220000000000−2222000000000000000000000000000
χ5144-44-4-4-44-4-4400004000000−22−222222000000000022−22000000000000000000000000000
χ524-444-44-4-44-440000-44-4-44000000000000000000000000000000000000000000000
χ534-444-44-4-44-440000-4-444-4000000000000000000000000000000000000000000000
χ544-444-44-4-4-44-400004000000000000000000000000002i2−2i2−2i22i20000000000000000000
χ554-444-44-4-4-44-40000400000000000000000000000000−2i22i22i2−2i20000000000000000000
χ564-44-4-4-4440000000000000022−2222−220000000000000022−2200002-22-2000000000000000
χ574-44-4-4-4440000000000000022−2222−2200000000000000−22220000-22-22000000000000000
χ584-44-4-4-44400000000000000−2222−22220000000000000022−220000-22-22000000000000000
χ594-44-4-4-44400000000000000−2222−222200000000000000−222200002-22-2000000000000000
χ604-4-444-44-4-44444-4-4-400004-40000000000000000000000000000000000000000000
χ614-4-4-444-440004-4-4400000004-4-44000000000000000000000000000000000000000
χ624-4-4-444-440004-4-440000000-444-4000000000000000000000000000000000000000
χ634-4-4-444-44000-444-4000000000000000000000000000000022−22−2222000000000000000
χ644-4-4-444-44000-444-40000000000000000000000000000000−222222−22000000000000000
χ6588-8-8-888-8000000000000000000000000000000000000000000000000000000000

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