Finite Group Databasebeta

← Group #112681

Character table — Group #112681

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222244444444444444442444888888888888888888888888888888882222444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111111-1-1-1-1
χ91111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-11111−i−iii−i−iii
χ111111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−iii−i−iii
χ121111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111ii−i−iii−i−i
χ131111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iii
χ141111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iiiii−i−i
χ151111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i
χ161111-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i−i−iii
χ17222222222222-2-2-2-2-2-22222-2-2-2-2-2-22-22-2000000000000000000000000000000000000000000002i−2i2i−2i
χ18222222222222-2-2-2-2-2-22222-2-2-2-2-2-22-22-200000000000000000000000000000000000000000000−2i2i−2i2i
χ192222222222-2-22222-2-2-2-2222222-2-2-2-2-2-200000000000000000000000022-2-222-2-20000000000000000
χ202222222222-2-22222-2-2-2-2222222-2-2-2-2-2-2000000000000000000000000-2-222-2-2220000000000000000
χ212222222222-2-2-2-2-2-222-2-222-2-2-2-222-22-22000000000000000000000000000000002-2002-20000000000
χ222222222222-2-2-2-2-2-222-2-222-2-2-2-222-22-2200000000000000000000000000000000-2200-220000000000
χ2322222222-2-22222-2-22222-2-222-2-222-2-2-2-200000000000000000000000000000000000000002-22-20000
χ2422222222-2-22222-2-22222-2-222-2-222-2-2-2-20000000000000000000000000000000000000000-22-220000
χ2522222222-2-222-2-222-2-222-2-2-2-222-2-2-22-222222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ2622222222-2-222-2-222-2-222-2-2-2-222-2-2-22-22-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ2722222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-2222200000000000000000000000000000000002-2002-200000000
χ2822222222-2-2-2-222-2-2-2-2-2-2-2-222-2-2-2-222220000000000000000000000000000000000-2200-2200000000
χ2922222222-2-2-2-2-2-22222-2-2-2-2-2-222222-22-2000000000000000022-2-222-2-2000000000000000000000000
χ3022222222-2-2-2-2-2-22222-2-2-2-2-2-222222-22-20000000000000000-2-222-2-222000000000000000000000000
χ312222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-22222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ322222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-22222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ332222-2-2-2-22222-2-2-2-222-2-2-2-22222-2-22-2-22000000000000000000000000000000002-200-220000000000
χ342222-2-2-2-22222-2-2-2-222-2-2-2-22222-2-22-2-2200000000000000000000000000000000-22002-20000000000
χ352222-2-2-2-222-2-2-2-2-2-2-2-222-2-2222222-222-2000000000000000000000000000000000000000000002-2-22
χ362222-2-2-2-222-2-2-2-2-2-2-2-222-2-2222222-222-200000000000000000000000000000000000000000000-222-2
χ372222-2-2-2-2-2-22222-2-2-2-2-2-222-2-22222-2-22200000000000000000000000000000000002-200-2200000000
χ382222-2-2-2-2-2-22222-2-2-2-2-2-222-2-22222-2-2220000000000000000000000000000000000-22002-200000000
χ392222-2-2-2-2-2-222-2-22222-2-22222-2-2-2-2-222-200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ402222-2-2-2-2-2-222-2-22222-2-22222-2-2-2-2-222-20000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ412222-2-2-2-2-2-2-2-222-2-2222222-2-222-2-222-2-200000000000000000000000000000000000000002i−2i−2i2i0000
χ422222-2-2-2-2-2-2-2-222-2-2222222-2-222-2-222-2-20000000000000000000000000000000000000000−2i2i2i−2i0000
χ432222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2222-2-222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000
χ442222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2222-2-22-2-2-2-222222222-2-2-2-200000000000000000000000000000000
χ4522-2-22i2i−2i−2i2-2002-22-200002i−2i2i−2i2i−2i00000022−2−222−2−2i2i2−i2−i2i2i2−i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ−2ζ002ζ3−2ζ30000000000000000
χ4622-2-22i2i−2i−2i2-2002-22-200002i−2i2i−2i2i−2i00000022−2−222−2−2i2i2−i2−i2i2i2−i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ2ζ00−2ζ32ζ30000000000000000
χ4722-2-22i2i−2i−2i2-2002-22-200002i−2i2i−2i2i−2i000000−2−222−2−222−i2−i2i2i2−i2−i2i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ2ζ00−2ζ32ζ30000000000000000
χ4822-2-22i2i−2i−2i2-2002-22-200002i−2i2i−2i2i−2i000000−2−222−2−222−i2−i2i2i2−i2−i2i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ−2ζ002ζ3−2ζ30000000000000000
χ4922-2-22i2i−2i−2i-2200-222-20000−2i2i−2i2i2i−2i00000022−2−2−2−222i2i2−i2−i2−i2−i2i2i21+i−1−i−1−i1+i1−i−1+i−1+i1−i2ζ−2ζ002ζ3−2ζ3000000000000000000
χ5022-2-22i2i−2i−2i-2200-222-20000−2i2i−2i2i2i−2i00000022−2−2−2−222i2i2−i2−i2−i2−i2i2i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i−2ζ2ζ00−2ζ32ζ3000000000000000000
χ5122-2-22i2i−2i−2i-2200-222-20000−2i2i−2i2i2i−2i000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i21+i−1−i−1−i1+i1−i−1+i−1+i1−i−2ζ2ζ00−2ζ32ζ3000000000000000000
χ5222-2-22i2i−2i−2i-2200-222-20000−2i2i−2i2i2i−2i000000−2−22222−2−2−i2−i2i2i2i2i2−i2−i2−1−i1+i1+i−1−i−1+i1−i1−i−1+i2ζ−2ζ002ζ3−2ζ3000000000000000000
χ5322-2-2−2i−2i2i2i2-2002-22-20000−2i2i−2i2i−2i2i00000022−2−222−2−2−i2−i2i2i2−i2−i2i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ32ζ300−2ζ2ζ0000000000000000
χ5422-2-2−2i−2i2i2i2-2002-22-20000−2i2i−2i2i−2i2i00000022−2−222−2−2−i2−i2i2i2−i2−i2i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ3−2ζ3002ζ−2ζ0000000000000000
χ5522-2-2−2i−2i2i2i2-2002-22-20000−2i2i−2i2i−2i2i000000−2−222−2−222i2i2−i2−i2i2i2−i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ3−2ζ3002ζ−2ζ0000000000000000
χ5622-2-2−2i−2i2i2i2-2002-22-20000−2i2i−2i2i−2i2i000000−2−222−2−222i2i2−i2−i2i2i2−i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ32ζ300−2ζ2ζ0000000000000000
χ5722-2-2−2i−2i2i2i-2200-222-200002i−2i2i−2i−2i2i00000022−2−2−2−222−i2−i2i2i2i2i2−i2−i21−i−1+i−1+i1−i1+i−1−i−1−i1+i−2ζ32ζ300−2ζ2ζ000000000000000000
χ5822-2-2−2i−2i2i2i-2200-222-200002i−2i2i−2i−2i2i00000022−2−2−2−222−i2−i2i2i2i2i2−i2−i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i2ζ3−2ζ3002ζ−2ζ000000000000000000
χ5922-2-2−2i−2i2i2i-2200-222-200002i−2i2i−2i−2i2i000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i21−i−1+i−1+i1−i1+i−1−i−1−i1+i2ζ3−2ζ3002ζ−2ζ000000000000000000
χ6022-2-2−2i−2i2i2i-2200-222-200002i−2i2i−2i−2i2i000000−2−22222−2−2i2i2−i2−i2−i2−i2i2i2−1+i1−i1−i−1+i−1−i1+i1+i−1−i−2ζ32ζ300−2ζ2ζ000000000000000000
χ6144-4-44i4i−4i−4i4-400-44-4400004i−4i−4i4i−4i4i000000000000000000000000000000000000000000000000000000
χ6244-4-44i4i−4i−4i-44004-4-440000−4i4i4i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ6344-4-4−4i−4i4i4i4-400-44-440000−4i4i4i−4i4i−4i000000000000000000000000000000000000000000000000000000
χ6444-4-4−4i−4i4i4i-44004-4-4400004i−4i−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ654-44-44i−4i4i−4i000000004-4000000004i−4i00002-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ664-44-44i−4i4i−4i000000004-4000000004i−4i0000-22-22-22-22−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ674-44-44i−4i4i−4i00000000-4400000000−4i4i00002-22-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ684-44-44i−4i4i−4i00000000-4400000000−4i4i0000-22-222-22-2−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ694-44-4−4i4i−4i4i000000004-400000000−4i4i00002-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ704-44-4−4i4i−4i4i000000004-400000000−4i4i0000-22-22-22-222i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ714-44-4−4i4i−4i4i00000000-44000000004i−4i00002-22-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ724-44-4−4i4i−4i4i00000000-44000000004i−4i0000-22-222-22-22i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ734-4-444-4-44004-40000004-4000000000000000022−22−2222000022−22−222200000000000000000000000000000000
χ744-4-444-4-44004-40000004-40000000000000000−222222−220000−222222−2200000000000000000000000000000000
χ754-4-444-4-4400-44000000-4400000000000022−22−2222000022−22−2222000000000000000000000000000000000000
χ764-4-444-4-4400-44000000-44000000000000−222222−220000−222222−22000000000000000000000000000000000000
χ774-4-44-444-4004-4000000-4400000000000022−22−22220000−222222−22000000000000000000000000000000000000
χ784-4-44-444-4004-4000000-44000000000000−222222−22000022−22−2222000000000000000000000000000000000000
χ794-4-44-444-400-440000004-4000000000000000022−22−22220000−222222−2200000000000000000000000000000000
χ804-4-44-444-400-440000004-40000000000000000−222222−22000022−22−222200000000000000000000000000000000

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