Finite Group Databasebeta

← Group #298387

Character table — Group #298387

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444488888888888888888888888888888888888881616161616163232
order12222222444444444444444444222222222222488888888888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ3111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111
χ511111111111111111111111111-1-1-1-11111-1-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1
χ611111111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1
χ91111111111-1-1-1-11111111-1-1-1-11111111-1-111-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11-11-11-1
χ101111111111-1-1-1-11111111-1-1-1-11111111-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-11-11-1-11
χ111111111111-1-1-1-11111111-1-1-1-111111-1-111-1-111-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-11-11-11
χ121111111111-1-1-1-11111111-1-1-1-111111-1-111-1-111-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-11-111-1
χ131111111111-1-1-1-11111111-1-1-1-11-1-1-1-111-1-1-1-111-11111-1-1-1-1-1-1-1-111111111-1-1-1-1111-1-11-11
χ141111111111-1-1-1-11111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111-1-111-1
χ151111111111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111-111-11-1
χ161111111111-1-1-1-11111111-1-1-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-111-1-11
χ1722222222222222-2-222-2-2-222-2-2-2000000002222-20000000000000000000000000000-2-200
χ1822222222222222-2-222-2-2-222-2-2-200000000-2-2-2-2-200000000000000000000000000002200
χ192222222222-2-2-2-2-2-222-2-2-2-2-222-20000000022-2-220000000000000000000000000000-2200
χ202222222222-2-2-2-2-2-222-2-2-2-2-222-200000000-2-222200000000000000000000000000002-200
χ2122222222-2-2222222-2-222-2-2-222-2000022220000-200000000000000000000000000-2-20000
χ2222222222-2-2222222-2-222-2-2-222-20000-2-2-2-20000-200000000000000000000000000220000
χ2322222222-2-22222-2-2-2-2-2-22-2-2-2-2222-2-20000000020000000000000000000000002-2000000
χ2422222222-2-22222-2-2-2-2-2-22-2-2-2-22-2-222000000002000000000000000000000000-22000000
χ2522222222-2-2-2-2-2-222-2-222-222-2-2-2000022-2-20000200000000000000000000000000-220000
χ2622222222-2-2-2-2-2-222-2-222-222-2-2-20000-2-22200002000000000000000000000000002-20000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-200000000-2000000000000000000000000-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-22200000000-20000000000000000000000002-2000000
χ2922-2-2-222-22222-2-200-2-20002-2000000000002-22-2000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i200000000
χ3022-2-2-222-22222-2-200-2-20002-2000000000002-22-2000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i200000000
χ3122-2-2-222-22222-2-200-2-20002-200000000000-22-22000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i200000000
χ3222-2-2-222-22222-2-200-2-20002-200000000000-22-22000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i200000000
χ3322-2-2-222-222-2-22200-2-2000-22000000000002-2-22000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i200000000
χ3422-2-2-222-222-2-22200-2-2000-22000000000002-2-22000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i200000000
χ3522-2-2-222-222-2-22200-2-2000-2200000000000-222-2000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i200000000
χ3622-2-2-222-222-2-22200-2-2000-2200000000000-222-2000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i200000000
χ372-22-2-22-22002-22-2-2-200220002-2000002-22-20000022−2−222−2−2000000002−22−22−22−200000000
χ382-22-2-22-22002-22-2-2-200220002-2000002-22-200000−2−222−2−22200000000−22−22−22−2200000000
χ392-22-2-22-22002-22-2-2-200220002-200000-22-220000022−2−222−2−200000000−22−22−22−2200000000
χ402-22-2-22-22002-22-2-2-200220002-200000-22-2200000−2−222−2−222000000002−22−22−22−200000000
χ412-22-2-22-2200-22-22-2-20022000-22000002-2-220000022−2−2−2−222000000002−22−2−22−2200000000
χ422-22-2-22-2200-22-22-2-20022000-22000002-2-2200000−2−22222−2−200000000−22−222−22−200000000
χ432-22-2-22-2200-22-22-2-20022000-2200000-222-20000022−2−2−2−22200000000−22−222−22−200000000
χ442-22-2-22-2200-22-22-2-20022000-2200000-222-200000−2−22222−2−2000000002−22−2−22−2200000000
χ452-2-22-2-2222-200002-22-22-2-2000022-22-200000000000002-22-200002-22-20000000000000000
χ462-2-22-2-2222-200002-22-22-2-2000022-22-20000000000000-22-220000-22-220000000000000000
χ472-2-22-2-2222-200002-22-22-2-200002-22-2200000000000002-22-20000-22-220000000000000000
χ482-2-22-2-2222-200002-22-22-2-200002-22-220000000000000-22-2200002-22-20000000000000000
χ492-2-22-2-222-220000-22-22-22-2000022-2-220000000002-22-200002-22-200000000000000000000
χ502-2-22-2-222-220000-22-22-22-2000022-2-22000000000-22-220000-22-2200000000000000000000
χ512-2-22-2-222-220000-22-22-22-200002-222-20000000002-22-20000-22-2200000000000000000000
χ522-2-22-2-222-220000-22-22-22-200002-222-2000000000-22-2200002-22-200000000000000000000
χ5344-4-44-4-440000004-400-44000000000000000000022−22−22220000000000000000000000000000
χ5444-4-44-4-440000004-400-440000000000000000000−222222−220000000000000000000000000000
χ5544-4-44-4-44000000-44004-40000000000000000000000022−22−2222000000000000000000000000
χ5644-4-44-4-44000000-44004-400000000000000000000000−222222−22000000000000000000000000
χ5744-4-4-444-4-4-444-4-40044000-44000000000000000000000000000000000000000000000000
χ5844-4-4-444-4-4-4-4-44400440004-4000000000000000000000000000000000000000000000000
χ594-44-44-44-44-4000000-440000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ604-44-44-44-44-4000000-44000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ614-44-44-44-4-440000004-4000000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ624-44-44-44-4-440000004-400000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ634-44-4-44-44004-44-44400-4-4000-440000000000000000000000000000000000000000000000
χ644-44-4-44-4400-44-444400-4-40004-40000000000000000000000000000000000000000000000
χ654-4-4444-4-4004-4-44000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i00000000
χ664-4-4444-4-4004-4-4400000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i00000000
χ674-4-4444-4-400-444-4000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000
χ684-4-4444-4-400-444-400000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000
χ694-4-44-4-4444-40000-444-4-4440000-4000000000000000000000000000000000000000000000
χ704-4-44-4-444-4400004-4-444-440000-4000000000000000000000000000000000000000000000
χ718888-8-8-8-8000000000000000000000000000000000000000000000000000000000000000

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