Finite Group Databasebeta

← Group #101366

Character table — Group #101366

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111111112222222244444444444444888888888888888888888816161616161616161616161616161616
order12222222444444444444448888888824444444448888888888884444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-111111-1-1-1-1ii−i−iiiii−i−i−i−i11-1-1ii−i−i11-1-1ii−i−i
χ1011111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-111111-1-1-1-1ii−i−iiiii−i−i−i−i-1-111−i−iii-1-111−i−iii
χ1111111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1-11-1-11111ii−i−i−i−i−i−iiiii11-1-1ii−i−i-1-111−i−iii
χ1211111111-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1-11-1-11111ii−i−i−i−i−i−iiiii-1-111−i−iii11-1-1ii−i−i
χ1311111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-111111-1-1-1-1−i−iii−i−i−i−iiiii11-1-1−i−iii11-1-1−i−iii
χ1411111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-111111-1-1-1-1−i−iii−i−i−i−iiiii-1-111ii−i−i-1-111ii−i−i
χ1511111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1-11-1-11111−i−iiiiiii−i−i−i−i11-1-1−i−iii-1-111ii−i−i
χ1611111111-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1-11-1-11111−i−iiiiiii−i−i−i−i-1-111ii−i−i11-1-1−i−iii
χ17222222222222222222-2-2-2-222222222-200-2000000-2-2-2-2000000000000000000000000
χ18222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-200-20000002222000000000000000000000000
χ192222222222-2-2-2-222-2-2222200000000-222-2-2-222-2-20000000000000000000000000000
χ202222222222-2-2-2-222-2-2222200000000-2-2-2-222-2-2220000000000000000000000000000
χ212222222222-2-2-2-222-2-2-2-2-2-200000000200200000000002i2i−2i−2i2i2i−2i−2i0000000000000000
χ222222222222-2-2-2-222-2-2-2-2-2-20000000020020000000000−2i−2i2i2i−2i−2i2i2i0000000000000000
χ2322222222-2-22222-2-2-2-222-2-200000000222-2-2-2-2-2220000000000000000000000000000
χ2422222222-2-22222-2-2-2-222-2-2000000002-2-2-22222-2-20000000000000000000000000000
χ2522222222-2-22222-2-2-2-2-2-22200000000-2002000000000022-2-2-2-2220000000000000000
χ2622222222-2-22222-2-2-2-2-2-22200000000-20020000000000-2-22222-2-20000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-2222i2i2i2i−2i−2i−2i−2i200-2000000−2i−2i2i2i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-222−2i−2i−2i−2i2i2i2i2i200-20000002i2i−2i−2i000000000000000000000000
χ2922-2-22-2-222i−2i2i2i−2i−2i2i−2i2-200002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000000000000000002−2i2−i21+i−1−i1−i−1+i
χ3022-2-22-2-222i−2i2i2i−2i−2i2i−2i2-200002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000000000000000000−22−i2i2−1−i1+i−1+i1−i
χ3122-2-22-2-222i−2i2i2i−2i−2i2i−2i2-20000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000000000000000002−2i2−i2−1−i1+i−1+i1−i
χ3222-2-22-2-222i−2i2i2i−2i−2i2i−2i2-20000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000000000000000000−22−i2i21+i−1−i1−i−1+i
χ3322-2-22-2-22−2i2i−2i−2i2i2i−2i2i2-200002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000000000000000002−2−i2i2−1+i1−i−1−i1+i
χ3422-2-22-2-22−2i2i−2i−2i2i2i−2i2i2-200002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000000000000000000−22i2−i21−i−1+i1+i−1−i
χ3522-2-22-2-22−2i2i−2i−2i2i2i−2i2i2-20000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000000000000000002−2−i2i21−i−1+i1+i−1−i
χ3622-2-22-2-22−2i2i−2i−2i2i2i−2i2i2-20000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000000000000000000−22i2−i2−1+i1−i−1−i1+i
χ372-222-2-2-222i−2i0000−2i2i002-22i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00002i−2i002-21−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ382-222-2-2-222i−2i0000−2i2i002-22i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−2i2i00-221−i−1+i1+i−1−i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ392-222-2-2-222i−2i0000−2i2i002-22i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002i−2i002-2−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ402-222-2-2-222i−2i0000−2i2i002-22i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−2i2i00-22−1+i1−i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ412-222-2-2-222i−2i0000−2i2i00-22−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i02-20002i−2i00−1+i1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ422-222-2-2-222i−2i0000−2i2i00-22−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0-22000−2i2i00−1+i1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ432-222-2-2-222i−2i0000−2i2i00-22−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i02-20002i−2i001−i−1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ442-222-2-2-222i−2i0000−2i2i00-22−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0-22000−2i2i001−i−1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ452-222-2-2-22−2i2i00002i−2i002-2−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00002i−2i00-221+i−1−i1−i−1+i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ462-222-2-2-22−2i2i00002i−2i002-2−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−2i2i002-21+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ472-222-2-2-22−2i2i00002i−2i002-2−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002i−2i00-22−1−i1+i−1+i1−i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ482-222-2-2-22−2i2i00002i−2i002-2−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−2i2i002-2−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ492-222-2-2-22−2i2i00002i−2i00-222i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i02-2000−2i2i00−1−i1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ502-222-2-2-22−2i2i00002i−2i00-222i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0-220002i−2i00−1−i1+i−1+i1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ512-222-2-2-22−2i2i00002i−2i00-222i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i02-2000−2i2i001+i−1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ522-222-2-2-22−2i2i00002i−2i00-222i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0-220002i−2i001+i−1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ5344-4-44-4-444i−4i−4i−4i4i4i4i−4i-4400000000000000000000000000000000000000000000000000
χ5444-4-44-4-44−4i4i4i4i−4i−4i−4i4i-4400000000000000000000000000000000000000000000000000
χ554-44-444-4-4004-44-4000000000000000000000000000000000000002i−2i2i−2i000000000000
χ564-44-444-4-4004-44-400000000000000000000000000000000000000−2i2i−2i2i000000000000
χ574-44-444-4-400-44-44000000000000000000000000000000000000002i−2i−2i2i000000000000
χ584-44-444-4-400-44-4400000000000000000000000000000000000000−2i2i2i−2i000000000000
χ594-4-444-44-4004i−4i−4i4i0000000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ604-4-444-44-4004i−4i−4i4i000000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ614-4-444-44-400−4i4i4i−4i0000000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ624-4-444-44-400−4i4i4i−4i000000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ634-4-4-4-4444440000-4-40000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000000000
χ644-4-4-4-4444440000-4-4000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000000000
χ654-4-4-4-4444-4-400004400000022−22−2222−222222−2200000000000000000000000000000000000000
χ664-4-4-4-4444-4-4000044000000−222222−2222−22−222200000000000000000000000000000000000000
χ67888-8-8-88-8000000000000000000000000000000000000000000000000000000000000
χ6888-88-88-8-8000000000000000000000000000000000000000000000000000000000000

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