Finite Group Databasebeta

← Group #134751

Character table — Group #134751

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size1111222222222222224444444444444444444444444444888888888888883232323232323232
order12222244448888888822222222444444448888888888884444448888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111111111-1-1-1111111-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ511111111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1111111-1-1-1-1
χ611111111111111111111-1-1-1-111111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1ii−i−i−i−iii
χ811111111111111111111-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1−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
χ111111111111-1-1-1-1-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111i−i−iii−i−ii
χ121111111111-1-1-1-1-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−iii−i−iii−i
χ131111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-11111-1-11-11-1-11-11
χ141111111111-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-1-11-1-1-1-11111111111-1-1-1-1-1-11111-1-1-11-111-11-1
χ151111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-111i−i−ii−iii−i
χ161111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-111−iii−ii−i−ii
χ17222222222222222222-2-2000022-2-2-20000-2-2-2-2-200000000-220000-2-200002200000000
χ18222222222222222222-2-20000-2-22-2-200002-2-2-2-2000000002-20000220000-2-200000000
χ192222222222-2-2-2-2-2-2-2-2-2-2000022-2-2-20000-2222200000000-220000220000-2-200000000
χ202222222222-2-2-2-2-2-2-2-2-2-20000-2-22-2-2000022222000000002-20000-2-200002200000000
χ21222222-2-2-2-200000000222222222-2-2-2-2-2-22000000000000-2-222-2-20000000000000000
χ22222222-2-2-2-200000000222222-2-2-2-2-2-2-2-2-2-200000000000022-2-2220000000000000000
χ23222222-2-2-2-20000000022-2-2-2-2222-2-222222000000000000-2-2-2-2220000000000000000
χ24222222-2-2-2-20000000022-2-2-2-2-2-2-2-2-22222-20000000000002222-2-20000000000000000
χ25222222-2-2-2-200000000-2-2000022-2220000-200002i2i2i2i−2i−2i−2i−2i2-20000002i2i−2i−2i0000000000
χ26222222-2-2-2-200000000-2-2000022-2220000-20000−2i−2i−2i−2i2i2i2i2i2-2000000−2i−2i2i2i0000000000
χ27222222-2-2-2-200000000-2-20000-2-22220000200002i2i2i2i−2i−2i−2i−2i-22000000−2i−2i2i2i0000000000
χ28222222-2-2-2-200000000-2-20000-2-2222000020000−2i−2i−2i−2i2i2i2i2i-220000002i2i−2i−2i0000000000
χ2922-2-22-200002222−2−2−2−22-200002-2-2002i2i−2i−2i222−2−2i2i2−i2−i2i2i2−i2−i200002i−2i2−2i2−i2i2−i22−200000000
χ3022-2-22-200002222−2−2−2−22-200002-2-200−2i−2i2i2i222−2−2−i2−i2i2i2−i2−i2i2i20000−2i2i2−2−i2i2−i2i22−200000000
χ3122-2-22-200002222−2−2−2−22-20000-222002i2i−2i−2i-222−2−2i2i2−i2−i2i2i2−i2−i20000−2i2i−22−i2i2−i2i2−2200000000
χ3222-2-22-200002222−2−2−2−22-20000-22200−2i−2i2i2i-222−2−2−i2−i2i2i2−i2−i2i2i200002i−2i−22i2−i2i2−i2−2200000000
χ3322-2-22-200002222−2−2−2−2-2222-2-22-22000000-2−2−22222−2−2−2−222002-200−222−2−222−200000000
χ3422-2-22-200002222−2−2−2−2-2222-2-2-22-20000002−2−22222−2−2−2−22200-22002−2−222−2−2200000000
χ3522-2-22-200002222−2−2−2−2-22-2-2222-22000000-2−2−222−2−22222−2−200-2200−22−222−22−200000000
χ3622-2-22-200002222−2−2−2−2-22-2-222-22-20000002−2−222−2−22222−2−2002-2002−22−2−22−2200000000
χ3722-2-22-20000−2−2−2−222222-200002-2-2002i2i−2i−2i2−2−222−i2−i2i2i2−i2−i2i2i200002i−2i−22−i2i2−i2i2−2200000000
χ3822-2-22-20000−2−2−2−222222-200002-2-200−2i−2i2i2i2−2−222i2i2−i2−i2i2i2−i2−i20000−2i2i−22i2−i2i2−i2−2200000000
χ3922-2-22-20000−2−2−2−222222-20000-222002i2i−2i−2i-2−2−222−i2−i2i2i2−i2−i2i2i20000−2i2i2−2i2−i2i2−i22−200000000
χ4022-2-22-20000−2−2−2−222222-20000-22200−2i−2i2i2i-2−2−222i2i2−i2−i2i2i2−i2−i200002i−2i2−2−i2i2−i2i22−200000000
χ4122-2-22-20000−2−2−2−22222-2222-2-22-22000000-222−2−2−2−22222−2−2002-2002−2−222−2−2200000000
χ4222-2-22-20000−2−2−2−22222-2222-2-2-22-2000000222−2−2−2−22222−2−200-2200−222−2−222−200000000
χ4322-2-22-20000−2−2−2−22222-22-2-2222-22000000-222−2−222−2−2−2−22200-22002−22−2−22−2200000000
χ4422-2-22-20000−2−2−2−22222-22-2-222-22-2000000222−2−222−2−2−2−222002-200−22−222−22−200000000
χ454444-4-444-4-40000000000000000000000004i−4i4i−4i000000000000000000000000000000
χ464444-4-444-4-4000000000000000000000000−4i4i−4i4i000000000000000000000000000000
χ474444-4-4-4-44444-4-444-4-400000000000000000000000000000000000000000000000000
χ484444-4-4-4-444-4-444-4-44400000000000000000000000000000000000000000000000000
χ4944-4-4-4400002222−22−22−22−2222220000000004i−4i000002i2−2i2−2i22i2000000000000000000000000000000
χ5044-4-4-4400002222−22−22−22−222222000000000−4i4i00000−2i22i22i2−2i2000000000000000000000000000000
χ5144-4-4-440000−22−2222222222−22−220000000004i−4i00000−2i22i22i2−2i2000000000000000000000000000000
χ5244-4-4-440000−22−2222222222−22−22000000000−4i4i000002i2−2i2−2i22i2000000000000000000000000000000
χ534-44-4004i−4i002i2−2i222−222i2−2i222−22002-22-2000002i−2i2i−2i000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000
χ544-44-4004i−4i002i2−2i222−222i2−2i222−2200-22-2200000−2i2i−2i2i00000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000
χ554-44-4004i−4i00−2i22i2−2222−2i22i2−2222002-22-2000002i−2i2i−2i00000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000000000000000000
χ564-44-4004i−4i00−2i22i2−2222−2i22i2−222200-22-2200000−2i2i−2i2i000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000000000000000
χ574-44-400−4i4i002i2−2i2−22222i2−2i2−2222002-22-200000−2i2i−2i2i000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000
χ584-44-400−4i4i002i2−2i2−22222i2−2i2−222200-22-22000002i−2i2i−2i00000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000
χ594-44-400−4i4i00−2i22i222−22−2i22i222−22002-22-200000−2i2i−2i2i00000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000000000000000000
χ604-44-400−4i4i00−2i22i222−22−2i22i222−2200-22-22000002i−2i2i−2i000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000000000000000000
χ614-4-4400004-44i−4i00−4i4i00002-2-2200000-222-2000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ624-4-4400004-44i−4i00−4i4i0000-222-2000002-2-2200000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ634-4-4400004-4−4i4i004i−4i00002-2-2200000-222-200000−2i2i2i−2i2i−2i−2i2i0000000000000000000000
χ644-4-4400004-4−4i4i004i−4i0000-222-2000002-2-22000002i−2i−2i2i−2i2i2i−2i0000000000000000000000
χ654-4-440000-44004-400-44002-2-22000002-2-22000002-2-222-2-220000000000000000000000
χ664-4-440000-44004-400-4400-222-200000-222-200000-222-2-222-20000000000000000000000
χ674-4-440000-4400-44004-4002-2-22000002-2-2200000-222-2-222-20000000000000000000000
χ684-4-440000-4400-44004-400-222-200000-222-2000002-2-222-2-220000000000000000000000

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