Finite Group Databasebeta

← Group #271070

Character table — Group #271070

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222224444444444444488888888888888888888888888161616161616161616163232
order12222222444444442244444444444422224444448888888888888888444444888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111-1-1-1-11-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ61111111111111111111111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1
χ71111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1
χ81111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ91111111111111111-1-1-1-11-1-1-1-111111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1111-1-111-1-11-1
χ101111111111111111-1-1-1-11-1-1-1-111111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-11
χ111111111111111111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11-1-1-111-1-111-11
χ121111111111111111-1-1-1-11-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-11-1
χ131111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111-1-1111-1
χ141111111111111111-1-1-1-11-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1-11111-1-1-11
χ151111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-111-1-1111111-1-1-1-1-1-1-1-111111-111-1-111-1-1-11
χ161111111111111111-1-1-1-11-1-1-1-1-1-1-1-1111-1-111-1-111-1-1-1-111111111-1-1-1-11-111-1-1-1-1111-1
χ172222222222-2-2-222-22222-2-2-2-2-22222-2-2-20000-2-2220000000000000000000000000000
χ182222222222-2-2-222-22222-2-2-2-2-2-2-2-2-2-222000022-2-20000000000000000000000000000
χ192222222222-2-2-222-2-2-2-2-2-222222222-2220000-2-2-2-20000000000000000000000000000
χ202222222222-2-2-222-2-2-2-2-2-22222-2-2-2-2-2-2-2000022220000000000000000000000000000
χ2122222222-2-2222-2-2222-2-2-222-2-20000-20022-2-2000000000000000000002-20000000000
χ2222222222-2-2222-2-2222-2-2-222-2-20000-200-2-22200000000000000000000-220000000000
χ2322222222-2-2222-2-22-2-222-2-2-2220000-200222200000000000000000000-2-20000000000
χ2422222222-2-2222-2-22-2-222-2-2-2220000-200-2-2-2-200000000000000000000220000000000
χ2522222222-2-2-2-2-2-2-2-222-2-22-2-2220000200000000000000000000000000002-22-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-22-2-222000020000000000000000000000000000-22-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222-2-20000200000000000000000000000000002-2-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222-2-2000020000000000000000000000000000-222-2000000
χ2922-2-222-2-22-20002-20000002i−2i2i−2i2i2i−2i−2i02-200000000i2i2−i2−i222−2−222−2−2i2i2−i2−i2000000000000
χ3022-2-222-2-22-20002-20000002i−2i2i−2i2i2i−2i−2i02-200000000−i2−i2i2i2−2−222−2−222−i2−i2i2i2000000000000
χ3122-2-222-2-22-20002-20000002i−2i2i−2i−2i−2i2i2i0-2200000000i2i2−i2−i222−2−2−2−222−i2−i2i2i2000000000000
χ3222-2-222-2-22-20002-20000002i−2i2i−2i−2i−2i2i2i0-2200000000−i2−i2i2i2−2−22222−2−2i2i2−i2−i2000000000000
χ3322-2-222-2-22-20002-2000000−2i2i−2i2i2i2i−2i−2i0-2200000000i2i2−i2−i2−2−22222−2−2−i2−i2i2i2000000000000
χ3422-2-222-2-22-20002-2000000−2i2i−2i2i2i2i−2i−2i0-2200000000−i2−i2i2i222−2−2−2−222i2i2−i2−i2000000000000
χ3522-2-222-2-22-20002-2000000−2i2i−2i2i−2i−2i2i2i02-200000000i2i2−i2−i2−2−222−2−222i2i2−i2−i2000000000000
χ3622-2-222-2-22-20002-2000000−2i2i−2i2i−2i−2i2i2i02-200000000−i2−i2i2i222−2−222−2−2−i2−i2i2i2000000000000
χ372-2222-2-2-2-2-20002202-22-2000002i−2i2i−2i0000000002i−2ii2−i2i2−i2i2−i2i2−i22−22−22−22−2000000000000
χ382-2222-2-2-2-2-20002202-22-2000002i−2i2i−2i0000000002i−2i−i2i2−i2i2−i2i2−i2i2−22−22−22−22000000000000
χ392-2222-2-2-2-2-20002202-22-200000−2i2i−2i2i000000000−2i2ii2−i2i2−i2i2−i2i2−i2−22−22−22−22000000000000
χ402-2222-2-2-2-2-20002202-22-200000−2i2i−2i2i000000000−2i2i−i2i2−i2i2−i2i2−i2i22−22−22−22−2000000000000
χ412-2222-2-2-2-2-2000220-22-22000002i−2i2i−2i000000000−2i2ii2−i2i2−i2−i2i2−i2i22−22−2−22−22000000000000
χ422-2222-2-2-2-2-2000220-22-22000002i−2i2i−2i000000000−2i2i−i2i2−i2i2i2−i2i2−i2−22−222−22−2000000000000
χ432-2222-2-2-2-2-2000220-22-2200000−2i2i−2i2i0000000002i−2ii2−i2i2−i2−i2i2−i2i2−22−222−22−2000000000000
χ442-2222-2-2-2-2-2000220-22-2200000−2i2i−2i2i0000000002i−2i−i2i2−i2i2i2−i2i2−i22−22−2−22−22000000000000
χ452-2-2-22-222-2222-22-2-20000200002-2-22-20000002-20000002i−2i−2i2i0000−2i2i2i−2i000000000000
χ462-2-2-22-222-2222-22-2-20000200002-2-22-20000002-2000000−2i2i2i−2i00002i−2i−2i2i000000000000
χ472-2-2-22-222-2222-22-2-2000020000-222-2-2000000-220000002i−2i−2i2i00002i−2i−2i2i000000000000
χ482-2-2-22-222-2222-22-2-2000020000-222-2-2000000-22000000−2i2i2i−2i0000−2i2i2i−2i000000000000
χ492-2-2-22-222-22-2-222-220000-200002-2-222000000-22002-2-2200002-2-220000000000000000
χ502-2-2-22-222-22-2-222-220000-200002-2-222000000-2200-222-20000-222-20000000000000000
χ512-2-2-22-222-22-2-222-220000-20000-222-220000002-2002-2-220000-222-20000000000000000
χ522-2-2-22-222-22-2-222-220000-20000-222-220000002-200-222-200002-2-220000000000000000
χ53444-4-4-44-4004-4400-400000000000000000000000000000000000000000000000022−2200
χ54444-4-4-44-4004-4400-4000000000000000000000000000000000000000000000000−222200
χ55444-4-4-44-400-44-400400000000000000000000000000000000000000000000002i2−2i20000
χ56444-4-4-44-400-44-40040000000000000000000000000000000000000000000000−2i22i20000
χ5744-4-444-4-4-44000-440000004i−4i−4i4i0000000000000000000000000000000000000000000
χ5844-4-444-4-4-44000-44000000−4i4i4i−4i0000000000000000000000000000000000000000000
χ594-4444-4-4-444000-4-404-4-44000000000000000000000000000000000000000000000000
χ604-4444-4-4-444000-4-40-444-4000000000000000000000000000000000000000000000000
χ614-4-44-444-4004-4-400400000000000000004-40000000000000000000000000000000000
χ624-4-44-444-4004-4-40040000000000000000-440000000000000000000000000000000000
χ634-4-44-444-400-44400-40000000000000000004i−4i00000000000000000000000000000000
χ644-4-44-444-400-44400-4000000000000000000−4i4i00000000000000000000000000000000
χ654-4-4-44-4444-444-4-44-40000-400000000400000000000000000000000000000000000000
χ664-4-4-44-4444-4-4-44-4440000400000000-400000000000000000000000000000000000000
χ6788-88-8-8-88000000000000000000000000000000000000000000000000000000000000
χ688-88-8-88-88000000000000000000000000000000000000000000000000000000000000

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