Finite Group Databasebeta

← Group #134815

Character table — Group #134815

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222224444444444444444444444444444888888888888883232323232323232
order12222244448888888844444444444444448888888888882244448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111ii−i−i−i−iii
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111−i−iiiii−i−i
χ91111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-11-11-11-1
χ101111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-11-11-11
χ111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111i−ii−i−ii−ii
χ121111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−ii−iii−ii−i
χ131111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-111111-1-111-1-11
χ141111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-11111-111-1-111-1
χ151111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1i−i−ii−iii−i
χ161111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111111-1-1-1-1−iii−ii−i−ii
χ17222222222222222222-2-2-2-20000000022-2-200000000-2-2-2-2002-20022-2-2000000000000
χ18222222222222222222-2-2-2-200000000-2-22200000000-2-2-2-200-2200-2-222000000000000
χ192222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-2000000002222002-200-2-222000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-2-2-200000000-2-22200000000222200-220022-2-2000000000000
χ21222222-2-2-2-20000000022-2-20000000022-2-22i2i2i2i−2i−2i−2i−2i000000-220000002i2i−2i−2i00000000
χ22222222-2-2-2-20000000022-2-20000000022-2-2−2i−2i−2i−2i2i2i2i2i000000-22000000−2i−2i2i2i00000000
χ23222222-2-2-2-20000000022-2-200000000-2-2222i2i2i2i−2i−2i−2i−2i0000002-2000000−2i−2i2i2i00000000
χ24222222-2-2-2-20000000022-2-200000000-2-222−2i−2i−2i−2i2i2i2i2i0000002-20000002i2i−2i−2i00000000
χ25222222-2-2-2-200000000-2-2222222-2-2-2-2222200000000000022-2-2-2-20000000000000000
χ26222222-2-2-2-200000000-2-2222222-2-2-2-2-2-2-2-2000000000000-2-222220000000000000000
χ27222222-2-2-2-200000000-2-222-2-2-2-222222222000000000000-2-2-2-2220000000000000000
χ28222222-2-2-2-200000000-2-222-2-2-2-22222-2-2-2-20000000000002222-2-20000000000000000
χ2922-2-22-200002222−2−2−2−2002-2000022-2-22i−2i2i−2i22−2−222−2−222−2−200002i−2ii2−i2i2−i2i2−i2i2−i200000000
χ3022-2-22-200002222−2−2−2−2002-2000022-2-2−2i2i−2i2i22−2−222−2−222−2−20000−2i2i−i2i2−i2i2−i2i2−i2i200000000
χ3122-2-22-200002222−2−2−2−2002-20000-2-2222i−2i2i−2i−2−222−2−22222−2−20000−2i2ii2−i2i2−i2−i2i2−i2i200000000
χ3222-2-22-200002222−2−2−2−2002-20000-2-222−2i2i−2i2i−2−222−2−22222−2−200002i−2i−i2i2−i2i2i2−i2i2−i200000000
χ3322-2-22-200002222−2−2−2−200-222i2i−2i−2i00002i−2i−2i2ii2i2−i2−i2−i2−i2i2i2−2−2222-20000i2−i2−i2i2−222−200000000
χ3422-2-22-200002222−2−2−2−200-222i2i−2i−2i0000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2−2−222-220000−i2i2i2−i22−2−2200000000
χ3522-2-22-200002222−2−2−2−200-22−2i−2i2i2i00002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2−2−222-220000i2−i2−i2i22−2−2200000000
χ3622-2-22-200002222−2−2−2−200-22−2i−2i2i2i0000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i2−2−2222-20000−i2i2i2−i2−222−200000000
χ3722-2-22-20000−2−2−2−22222002-2000022-2-22i−2i2i−2i−2−222−2−222−2−22200002i−2i−i2i2−i2i2−i2i2−i2i200000000
χ3822-2-22-20000−2−2−2−22222002-2000022-2-2−2i2i−2i2i−2−222−2−222−2−2220000−2i2ii2−i2i2−i2i2−i2i2−i200000000
χ3922-2-22-20000−2−2−2−22222002-20000-2-2222i−2i2i−2i22−2−222−2−2−2−2220000−2i2i−i2i2−i2i2i2−i2i2−i200000000
χ4022-2-22-20000−2−2−2−22222002-20000-2-222−2i2i−2i2i22−2−222−2−2−2−22200002i−2ii2−i2i2−i2−i2i2−i2i200000000
χ4122-2-22-20000−2−2−2−2222200-222i2i−2i−2i00002i−2i−2i2i−i2−i2i2i2i2i2−i2−i222−2−22-20000−i2i2i2−i22−2−2200000000
χ4222-2-22-20000−2−2−2−2222200-222i2i−2i−2i0000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i222−2−2-220000i2−i2−i2i2−222−200000000
χ4322-2-22-20000−2−2−2−2222200-22−2i−2i2i2i00002i−2i−2i2ii2i2−i2−i2−i2−i2i2i222−2−2-220000−i2i2i2−i2−222−200000000
χ4422-2-22-20000−2−2−2−2222200-22−2i−2i2i2i0000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i222−2−22-20000i2−i2−i2i22−2−2200000000
χ454444-4-444-4-4000000000000000000000000000000004i−4i4i−4i0000000000000000000000
χ464444-4-444-4-400000000000000000000000000000000−4i4i−4i4i0000000000000000000000
χ474444-4-4-4-44444-4-444-4-400000000000000000000000000000000000000000000000000
χ484444-4-4-4-444-4-444-4-44400000000000000000000000000000000000000000000000000
χ4944-4-4-4400002222−22−22−22−2222224i−4i00000000000000000000002i2−2i2−2i22i20000000000000000000000
χ5044-4-4-4400002222−22−22−22−222222−4i4i0000000000000000000000−2i22i22i2−2i20000000000000000000000
χ5144-4-4-440000−22−2222222222−22−224i−4i0000000000000000000000−2i22i22i2−2i20000000000000000000000
χ5244-4-4-440000−22−2222222222−22−22−4i4i00000000000000000000002i2−2i2−2i22i20000000000000000000000
χ534-44-400004-4004-4004-400002i−2i2i−2i2i−2i2i−2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ544-44-400004-4004-4004-40000−2i2i−2i2i−2i2i−2i2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ554-44-400004-400-4400-4400002i−2i2i−2i2i−2i2i−2i0000−2i2i−2i2i−2i2i−2i2i00000000000000000000000000
χ564-44-400004-400-4400-440000−2i2i−2i2i−2i2i−2i2i00002i−2i2i−2i2i−2i2i−2i00000000000000000000000000
χ574-44-40000-444i−4i004i−4i0000002i−2i2i−2i−2i2i−2i2i00002-22-2-22-2200000000000000000000000000
χ584-44-40000-444i−4i004i−4i000000−2i2i−2i2i2i−2i2i−2i0000-22-222-22-200000000000000000000000000
χ594-44-40000-44−4i4i00−4i4i0000002i−2i2i−2i−2i2i−2i2i0000-22-222-22-200000000000000000000000000
χ604-44-40000-44−4i4i00−4i4i000000−2i2i−2i2i2i−2i2i−2i00002-22-2-22-2200000000000000000000000000
χ614-4-44004i−4i002i2−2i222−22−2i22i2−222200002-2-22−2i2i2i−2i0000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000
χ624-4-44004i−4i002i2−2i222−22−2i22i2−22220000-222-22i−2i−2i2i00002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000
χ634-4-44004i−4i00−2i22i2−22222i2−2i222−2200002-2-22−2i2i2i−2i00002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000000000000000
χ644-4-44004i−4i00−2i22i2−22222i2−2i222−220000-222-22i−2i−2i2i0000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000000000000000
χ654-4-4400−4i4i002i2−2i2−2222−2i22i222−2200002-2-222i−2i−2i2i0000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000
χ664-4-4400−4i4i002i2−2i2−2222−2i22i222−220000-222-2−2i2i2i−2i00002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000
χ674-4-4400−4i4i00−2i22i222−222i2−2i2−222200002-2-222i−2i−2i2i00002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000000000000000
χ684-4-4400−4i4i00−2i22i222−222i2−2i2−22220000-222-2−2i2i2i−2i0000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000000000000000

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