Finite Group Databasebeta

← Group #134597

Character table — Group #134597

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222222224444444444444444444444161616161616161616161616161616161616161616161616
order124422244488888888888844444444444488888888884444888816161616161616161616161616161616
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ811111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ91111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111-1-1−i−iii−i−iii−i−iii−i−iii
χ111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111ii−i−iii−i−i−i−iii−i−iii
χ121111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-111−i−iii−i−iiiii−i−iii−i−i
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222-2-2222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-222-2-222000000000000000000000000
χ18222222222222-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-2222222-2-2-2-2000000000000000000000000
χ192222222222-2-2222222-2-222-2-2-2-22222-2-2-2-2-2-2-2-2-2-22222000000000000000000000000
χ202222222222-2-222-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-222-2-2000000000000000000000000
χ2122-2-22-2-222-2002222-2-200-2-2000022-2-200000000002-22-2000000002−22−22−22−200000000
χ2222-2-22-2-222-2002222-2-200-2-2000022-2-200000000002-22-200000000−22−22−22−2200000000
χ2322-2-22-2-222-20022-2-22200-2-20000-2-22200000000002-2-22000000002−22−2−22−2200000000
χ2422-2-22-2-222-20022-2-22200-2-20000-2-22200000000002-2-2200000000−22−222−22−200000000
χ2522-2-22-2-222-200-2-222-2-200220000-2-2220000000000-222-200000000i2−i2−i2i2i2−i2−i2i200000000
χ2622-2-22-2-222-200-2-222-2-200220000-2-2220000000000-222-200000000−i2i2i2−i2−i2i2i2−i200000000
χ2722-2-22-2-222-200-2-2-2-2220022000022-2-20000000000-22-2200000000i2−i2−i2i2−i2i2i2−i200000000
χ2822-2-22-2-222-200-2-2-2-2220022000022-2-20000000000-22-2200000000−i2i2i2−i2i2−i2−i2i200000000
χ2922-2-2-22-22-22220022-2-2-2-20022-2-20000000000002-200-2200000000000000002−22−22−22−2
χ3022-2-2-22-22-22220022-2-2-2-20022-2-20000000000002-200-220000000000000000−22−22−22−22
χ3122-2-2-22-22-222200-2-222-2-200-2-2220000000000002-2002-200000000000000002−22−2−22−22
χ3222-2-2-22-22-222200-2-222-2-200-2-2220000000000002-2002-20000000000000000−22−222−22−2
χ3322-2-2-22-22-22-2-20022-2-22200-2-222000000000000-2200-220000000000000000i2−i2−i2i2i2−i2−i2i2
χ3422-2-2-22-22-22-2-20022-2-22200-2-222000000000000-2200-220000000000000000−i2i2i2−i2−i2i2i2−i2
χ3522-2-2-22-22-22-2-200-2-222220022-2-2000000000000-22002-20000000000000000i2−i2−i2i2−i2i2i2−i2
χ3622-2-2-22-22-22-2-200-2-222220022-2-2000000000000-22002-20000000000000000−i2i2i2−i2i2−i2−i2i2
χ3722-2-2-2-22-22222220000-2-2-2-20000000022-2-20000-22-22002-22-200000000000000000000
χ3822-2-2-2-22-22222220000-2-2-2-20000000022-2-20000-22-2200-22-2200000000000000000000
χ3922-2-2-2-22-22222-2-20000-2-22200000000-2-2220000-222-20000002i−2i2i−2i0000000000000000
χ4022-2-2-2-22-22222-2-20000-2-22200000000-2-2220000-222-2000000−2i2i−2i2i0000000000000000
χ4122-2-2-2-22-222-2-222000022-2-200000000-2-22200002-2-220000002i−2i−2i2i0000000000000000
χ4222-2-2-2-22-222-2-222000022-2-200000000-2-22200002-2-22000000−2i2i2i−2i0000000000000000
χ4322-2-2-2-22-222-2-2-2-2000022220000000022-2-200002-22-2002-2-2200000000000000000000
χ4422-2-2-2-22-222-2-2-2-2000022220000000022-2-200002-22-200-222-200000000000000000000
χ4544444-4-4-4-444400000044000000000000000000-4-40000000000000000000000000000
χ4644444-4-4-4-44-4-4000000-4-4000000000000000000440000000000000000000000000000
χ474444-44-4-44-4004400000044000000000000000000-4-400000000000000000000000000
χ484444-44-4-44-400-4-4000000-4-40000000000000000004400000000000000000000000000
χ494444-4-444-4-400004444000000000000000000000000-4-4000000000000000000000000
χ504444-4-444-4-40000-4-4-4-400000000000000000000000044000000000000000000000000
χ5144-4-4444-4-4-40000000000000000000000004i4i−4i−4i000000000000000000000000000000
χ5244-4-4444-4-4-4000000000000000000000000−4i−4i4i4i000000000000000000000000000000
χ534-44i−4i0000002i2−2i222−222i2−2i222−2222−222i2−2i22-22i−2i2i−2i2-22i−2i2-22ζ−2ζ2ζ3−2ζ3000000000000000000000000000000
χ544-44i−4i0000002i2−2i222−22−2i22i2−222222−222i2−2i2-22−2i2i−2i2i-222i−2i2-2−2ζ2ζ−2ζ32ζ3000000000000000000000000000000
χ554-44i−4i0000002i2−2i2−22222i2−2i222−2222−22−2i22i22-22i−2i−2i2i-22−2i2i-22−2ζ2ζ−2ζ32ζ3000000000000000000000000000000
χ564-44i−4i0000002i2−2i2−2222−2i22i2−222222−22−2i22i2-22−2i2i2i−2i2-2−2i2i-222ζ−2ζ2ζ3−2ζ3000000000000000000000000000000
χ574-44i−4i000000−2i22i222−222i2−2i222−22−22222i2−2i2-22−2i2i2i−2i2-2−2i2i-22−2ζ2ζ−2ζ32ζ3000000000000000000000000000000
χ584-44i−4i000000−2i22i222−22−2i22i2−2222−22222i2−2i22-22i−2i−2i2i-22−2i2i-222ζ−2ζ2ζ3−2ζ3000000000000000000000000000000
χ594-44i−4i000000−2i22i2−22222i2−2i222−22−2222−2i22i2-22−2i2i−2i2i-222i−2i2-22ζ−2ζ2ζ3−2ζ3000000000000000000000000000000
χ604-44i−4i000000−2i22i2−2222−2i22i2−2222−2222−2i22i22-22i−2i2i−2i2-22i−2i2-2−2ζ2ζ−2ζ32ζ3000000000000000000000000000000
χ614-4−4i4i0000002i2−2i222−222i2−2i2−2222−2222−2i22i22-2−2i2i2i−2i-222i−2i-22−2ζ32ζ3−2ζ2ζ000000000000000000000000000000
χ624-4−4i4i0000002i2−2i222−22−2i22i222−22−2222−2i22i2-222i−2i−2i2i2-22i−2i-222ζ3−2ζ32ζ−2ζ000000000000000000000000000000
χ634-4−4i4i0000002i2−2i2−22222i2−2i2−2222−22222i2−2i22-2−2i2i−2i2i2-2−2i2i2-22ζ3−2ζ32ζ−2ζ000000000000000000000000000000
χ644-4−4i4i0000002i2−2i2−2222−2i22i222−22−22222i2−2i2-222i−2i2i−2i-22−2i2i2-2−2ζ32ζ3−2ζ2ζ000000000000000000000000000000
χ654-4−4i4i000000−2i22i222−222i2−2i2−222222−22−2i22i2-222i−2i2i−2i-22−2i2i2-22ζ3−2ζ32ζ−2ζ000000000000000000000000000000
χ664-4−4i4i000000−2i22i222−22−2i22i222−2222−22−2i22i22-2−2i2i−2i2i2-2−2i2i2-2−2ζ32ζ3−2ζ2ζ000000000000000000000000000000
χ674-4−4i4i000000−2i22i2−22222i2−2i2−222222−222i2−2i2-222i−2i−2i2i2-22i−2i-22−2ζ32ζ3−2ζ2ζ000000000000000000000000000000
χ684-4−4i4i000000−2i22i2−2222−2i22i222−2222−222i2−2i22-2−2i2i2i−2i-222i−2i-222ζ3−2ζ32ζ−2ζ000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.