Finite Group Databasebeta

← Group #293595

Character table — Group #293595

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444444444444444444422444444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ3111111111111111111111111111111-1-11111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-111
χ6111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-111111-1-1
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11111-11111-1-1
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11111-1-1-1-1-111
χ91111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1111-1-11-1
χ101111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-11-1-111-11
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11-1-111-1-1-111-11
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-111-111-1-11-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1111-1-1111-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-111111-1-1-11
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-11111111-1-1-111-1-1-11
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111111111-1-1-1-1111-1-1-1-1-1111-1
χ172222222222-2-222-2-22222-2-2-2-20000-2-222000022000000000000000000-20000-2000000
χ182222222222-2-222-2-22222-2-2-2-20000-2-2-2-20000-2-2000000000000000000200002000000
χ192222222222-2-222-2-2-2-2-2-222220000-2-2220000-2-200000000000000000020000-2000000
χ202222222222-2-222-2-2-2-2-2-222220000-2-2-2-2000022000000000000000000-200002000000
χ2122222222-2-222-2-22222-2-222-2-22222-2-20022-2-200-2-20000000000000000000000000000
χ2222222222-2-222-2-22222-2-222-2-2-2-2-2-2-2-200-2-22200220000000000000000000000000000
χ2322222222-2-222-2-222-2-222-2-2222222-2-200-2-2-2-200220000000000000000000000000000
χ2422222222-2-222-2-222-2-222-2-222-2-2-2-2-2-200222200-2-20000000000000000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2-2-2220000220000000000000000000000000002-22-20000000
χ2622222222-2-2-2-2-2-2-2-222-2-2-2-222000022000000000000000000000000000-22-220000000
χ2722222222-2-2-2-2-2-2-2-2-2-22222-2-20000220000000000000000000000000002-2-220000000
χ2822222222-2-2-2-2-2-2-2-2-2-22222-2-2000022000000000000000000000000000-222-20000000
χ2922-2-22-2-22002-2002-2002i−2i002i−2i2i2i−2i−2i00000000002-2i2i2−i2−i222−2−222−2−2i2i2−i2−i2000000000000
χ3022-2-22-2-22002-2002-2002i−2i002i−2i2i2i−2i−2i00000000002-2−i2−i2i2i2−2−222−2−222−i2−i2i2i2000000000000
χ3122-2-22-2-22002-2002-2002i−2i002i−2i−2i−2i2i2i0000000000-22i2i2−i2−i222−2−2−2−222−i2−i2i2i2000000000000
χ3222-2-22-2-22002-2002-2002i−2i002i−2i−2i−2i2i2i0000000000-22−i2−i2i2i2−2−22222−2−2i2i2−i2−i2000000000000
χ3322-2-22-2-22002-2002-200−2i2i00−2i2i2i2i−2i−2i0000000000-22i2i2−i2−i2−2−22222−2−2−i2−i2i2i2000000000000
χ3422-2-22-2-22002-2002-200−2i2i00−2i2i2i2i−2i−2i0000000000-22−i2−i2i2i222−2−2−2−222i2i2−i2−i2000000000000
χ3522-2-22-2-22002-2002-200−2i2i00−2i2i−2i−2i2i2i00000000002-2i2i2−i2−i2−2−222−2−222i2i2−i2−i2000000000000
χ3622-2-22-2-22002-2002-200−2i2i00−2i2i−2i−2i2i2i00000000002-2−i2−i2i2i222−2−222−2−2−i2−i2i2i2000000000000
χ372-22-2-22-22002-200-222i−2i002i−2i002-22-200002i−2i000000i2−i2i2−i22−22−2i2−i2i2−i22−22−2000000000000
χ382-22-2-22-22002-200-222i−2i002i−2i002-22-200002i−2i000000−i2i2−i2i2−22−22−i2i2−i2i2−22−22000000000000
χ392-22-2-22-22002-200-222i−2i002i−2i00-22-220000−2i2i000000i2−i2i2−i22−22−2−i2i2−i2i2−22−22000000000000
χ402-22-2-22-22002-200-222i−2i002i−2i00-22-220000−2i2i000000−i2i2−i2i2−22−22i2−i2i2−i22−22−2000000000000
χ412-22-2-22-22002-200-22−2i2i00−2i2i002-22-20000−2i2i000000i2−i2i2−i2−22−22i2−i2i2−i2−22−22000000000000
χ422-22-2-22-22002-200-22−2i2i00−2i2i002-22-20000−2i2i000000−i2i2−i2i22−22−2−i2i2−i2i22−22−2000000000000
χ432-22-2-22-22002-200-22−2i2i00−2i2i00-22-2200002i−2i000000i2−i2i2−i2−22−22−i2i2−i2i22−22−2000000000000
χ442-22-2-22-22002-200-22−2i2i00−2i2i00-22-2200002i−2i000000−i2i2−i2i22−22−2i2−i2i2−i2−22−22000000000000
χ452-2-22-2-2222-2222-2-2-2000000002i−2i−2i2i2-200002i−2i000000002-2-2200002i−2i−2i2i000000000000
χ462-2-22-2-2222-2222-2-2-2000000002i−2i−2i2i2-200002i−2i00000000-222-20000−2i2i2i−2i000000000000
χ472-2-22-2-2222-2222-2-2-200000000−2i2i2i−2i2-20000−2i2i000000002-2-220000−2i2i2i−2i000000000000
χ482-2-22-2-2222-2222-2-2-200000000−2i2i2i−2i2-20000−2i2i00000000-222-200002i−2i−2i2i000000000000
χ492-2-22-2-222-2222-22-2-2000000002i−2i−2i2i-220000−2i2i00002-2-220000−2i2i2i−2i0000000000000000
χ502-2-22-2-222-2222-22-2-2000000002i−2i−2i2i-220000−2i2i0000-222-200002i−2i−2i2i0000000000000000
χ512-2-22-2-222-2222-22-2-200000000−2i2i2i−2i-2200002i−2i00002-2-2200002i−2i−2i2i0000000000000000
χ522-2-22-2-222-2222-22-2-200000000−2i2i2i−2i-2200002i−2i0000-222-20000−2i2i2i−2i0000000000000000
χ53444-4-4-44-44-400-4400000000000000004-4000000000000000000000000000000000000
χ54444-4-4-44-44-400-440000000000000000-44000000000000000000000000000000000000
χ55444-4-4-44-4-44004-400000000000000000000004-4000000000000000000000000000000
χ56444-4-4-44-4-44004-40000000000000000000000-44000000000000000000000000000000
χ5744-4-44-4-4400-4400-44004i−4i00−4i4i00000000000000000000000000000000000000000000
χ5844-4-44-4-4400-4400-4400−4i4i004i−4i00000000000000000000000000000000000000000000
χ594-44-4-44-4400-44004-44i−4i00−4i4i0000000000000000000000000000000000000000000000
χ604-44-4-44-4400-44004-4−4i4i004i−4i0000000000000000000000000000000000000000000000
χ614-4-44-4-4444-4-4-44-444000000000000-4400000000000000000000000000000000000000
χ624-4-44-4-444-44-4-4-44440000000000004-400000000000000000000000000000000000000
χ634-4-4-4444-44400-4-4000000000000000000000000000000000000000000000000002i2−2i200
χ644-4-4-4444-44400-4-400000000000000000000000000000000000000000000000000−2i22i200
χ654-4-4-4444-4-4-4004400000000000000000000000000000000000000000000000022−220000
χ664-4-4-4444-4-4-40044000000000000000000000000000000000000000000000000−22220000
χ6788-88-88-8-8000000000000000000000000000000000000000000000000000000000000
χ688-8888-8-8-8000000000000000000000000000000000000000000000000000000000000

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