Finite Group Databasebeta

← Group #111182

Character table — Group #111182

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12224444222222444444444444444444444444888888884444888888888888888888888888888822444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ91111111111-1-1-1-11111-1-1-111-111-1-1-1iiii−i−i−i−i-11111-1-1-1-1ii−i−i11-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i1-11-1ii−i−i
χ101111111111-1-1-1-11111-1-1-111-111-1-1-1iiii−i−i−i−i-11111-1-1-1-1ii−i−i11-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-11-11−i−iii
χ111111111111-1-1-1-11111-1-1-111-111-1-1-1iiii−i−i−i−i-1-1-1-1-11111ii−i−i-1-1111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-11-11−i−iii
χ121111111111-1-1-1-11111-1-1-111-111-1-1-1iiii−i−i−i−i-1-1-1-1-11111ii−i−i-1-111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii1-11-1ii−i−i
χ131111111111-1-1-1-11111-1-1-111-111-1-1-1−i−i−i−iiiii-11111-1-1-1-1−i−iii11-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−iii
χ141111111111-1-1-1-11111-1-1-111-111-1-1-1−i−i−i−iiiii-11111-1-1-1-1−i−iii11-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-11-11ii−i−i
χ151111111111-1-1-1-11111-1-1-111-111-1-1-1−i−i−i−iiiii-1-1-1-1-11111−i−iii-1-1111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-11-11ii−i−i
χ161111111111-1-1-1-11111-1-1-111-111-1-1-1−i−i−i−iiiii-1-1-1-1-11111−i−iii-1-111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i1-11-1−i−iii
χ171111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-111-1-111-1-1-1ii−i−iii−i−i1-11-1i−ii−iii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-1-111-11-1
χ181111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-111-1-111-1-1-1ii−i−iii−i−i1-11-1i−ii−i−i−iii−i−iiiii−i−iii−i−i−i−iii−i−iii-111-1-11-11
χ191111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-111-1-111-1-1-1−i−iii−i−iii1-11-1−ii−iiii−i−iii−i−i−i−iii−i−iiiii−i−iii−i−i-111-1-11-11
χ201111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-111-1-111-1-1-1−i−iii−i−iii1-11-1−ii−ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-1-111-11-1
χ211111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1-111-1-111-1ii−i−iii−i−i-11-11i−ii−iii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii1-1-11-11-11
χ221111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1-111-1-111-1ii−i−iii−i−i-11-11i−ii−i−i−iii−i−iii−i−iii−i−iiiii−i−iii−i−i-111-11-11-1
χ231111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1-111-1-111-1−i−iii−i−iii-11-11−ii−iiii−i−iii−i−iii−i−iii−i−i−i−iii−i−iii-111-11-11-1
χ241111-1-1-1-111111111-1-1-1-1-1-1-1-11-111-1-1-111-1-111-1−i−iii−i−iii-11-11−ii−ii−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i1-1-11-11-11
χ251111-1-1-1-111-1-1-1-111-1-1111-1-111-1-1-11ii−i−i−i−iii1ii−i−i−i−iiii−i−iii−i−iiii−i−i−i−iii-1-11111-1-1-1-11111-1-111-1-1i−i−ii
χ261111-1-1-1-111-1-1-1-111-1-1111-1-111-1-1-11ii−i−i−i−iii1ii−i−i−i−iiii−i−iii−i−ii−i−iiiii−i−i-1-11111-1-111-1-1-1-111-1-111−iii−i
χ271111-1-1-1-111-1-1-1-111-1-1111-1-111-1-1-11ii−i−i−i−iii1−i−iiiii−i−ii−i−ii−iii−iii−i−i−i−iii11-1-1-1-111-1-11111-1-1-1-111−iii−i
χ281111-1-1-1-111-1-1-1-111-1-1111-1-111-1-1-11ii−i−i−i−iii1−i−iiiii−i−ii−i−ii−iii−i−i−iiiii−i−i11-1-1-1-11111-1-1-1-11111-1-1i−i−ii
χ291111-1-1-1-111-1-1-1-111-1-1111-1-111-1-1-11−i−iiiii−i−i1ii−i−i−i−iii−iii−ii−i−iiii−i−i−i−iii11-1-1-1-11111-1-1-1-11111-1-1−iii−i
χ301111-1-1-1-111-1-1-1-111-1-1111-1-111-1-1-11−i−iiiii−i−i1ii−i−i−i−iii−iii−ii−i−ii−i−iiiii−i−i11-1-1-1-111-1-11111-1-1-1-111i−i−ii
χ311111-1-1-1-111-1-1-1-111-1-1111-1-111-1-1-11−i−iiiii−i−i1−i−iiiii−i−i−iii−i−iii−iii−i−i−i−iii-1-11111-1-111-1-1-1-111-1-111i−i−ii
χ321111-1-1-1-111-1-1-1-111-1-1111-1-111-1-1-11−i−iiiii−i−i1−i−iiiii−i−i−iii−i−iii−i−i−iiiii−i−i-1-11111-1-1-1-11111-1-111-1-1−iii−i
χ3322222222222222-2-222222-2-22-2-2-2-2-222222222-200000000-2-2-2-2000000000000000000000000000000000000
χ3422222222222222-2-222222-2-22-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000000000000000000000000
χ352222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-22222i2i2i2i−2i−2i−2i−2i200000000−2i−2i2i2i000000000000000000000000000000000000
χ362222222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2222−2i−2i−2i−2i2i2i2i2i2000000002i2i−2i−2i000000000000000000000000000000000000
χ3722222222-2-22-2-2222-2-222-222-2-2-22-2-20000000022222-2-2-2-20000-2-22200000000000000000000000000000000
χ3822222222-2-22-2-2222-2-222-222-2-2-22-2-2000000002-2-2-2-22222000022-2-200000000000000000000000000000000
χ3922222222-2-22-2-22-2-2-2-222-2-2-2-222-22200000000-20000000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ4022222222-2-22-2-22-2-2-2-222-2-2-2-222-22200000000-2000000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ4122222222-2-2-222-222-2-2-2-22222-2-2-22200000000-2222222220000-2-2-2-200000000000000000000000000000000
χ4222222222-2-2-222-222-2-2-2-22222-2-2-22200000000-2-2-2-2-2-2-2-2-20000222200000000000000000000000000000000
χ4322222222-2-2-222-2-2-2-2-2-2-22-2-22222-2-20000000020000000000000000000000002-22-2-22-220000000000000000
χ4422222222-2-2-222-2-2-2-2-2-2-22-2-22222-2-2000000002000000000000000000000000-22-222-22-20000000000000000
χ452222-2-2-2-2222222-2-2-2-2-2-2-222-2-22-2-2222-2-222-2-2200000000-22-22000000000000000000000000000000000000
χ462222-2-2-2-2222222-2-2-2-2-2-2-222-2-22-2-22-2-222-2-2222000000002-22-2000000000000000000000000000000000000
χ472222-2-2-2-222-2-2-2-2-2-2-2-2222222-2222-22i2i−2i−2i−2i−2i2i2i-200000000−2i2i2i−2i000000000000000000000000000000000000
χ482222-2-2-2-222-2-2-2-2-2-2-2-2222222-2222-2−2i−2i2i2i2i2i−2i−2i-2000000002i−2i−2i2i000000000000000000000000000000000000
χ492222-2-2-2-2-2-22-2-222222-2-22-2-22-222-2200000000-22i2i−2i−2i−2i−2i2i2i0000−2i2i2i−2i00000000000000000000000000000000
χ502222-2-2-2-2-2-22-2-222222-2-22-2-22-222-2200000000-2−2i−2i2i2i2i2i−2i−2i00002i−2i−2i2i00000000000000000000000000000000
χ512222-2-2-2-2-2-22-2-22-2-222-2-222222-2-22-20000000020000000000000000000000002-2-222-2-220000000000000000
χ522222-2-2-2-2-2-22-2-22-2-222-2-222222-2-22-2000000002000000000000000000000000-222-2-222-20000000000000000
χ532222-2-2-2-2-2-2-222-2222222-2-2-2-2-22-22-20000000022i2i−2i−2i2i2i−2i−2i0000−2i2i−2i2i00000000000000000000000000000000
χ542222-2-2-2-2-2-2-222-2222222-2-2-2-2-22-22-2000000002−2i−2i2i2i−2i−2i2i2i00002i−2i2i−2i00000000000000000000000000000000
χ552222-2-2-2-2-2-2-222-2-2-22222-222-22-22-2200000000-20000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ562222-2-2-2-2-2-2-222-2-2-22222-222-22-22-2200000000-2000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ572-2-2222-2-22-222-2-2002-22-2-2002000002i−2i2i−2i2i−2i2i−2i00000000000000000i2−i2i2−i2i2−i2i2−i2000000002−22−22−22−200000000
χ582-2-2222-2-22-222-2-2002-22-2-2002000002i−2i2i−2i2i−2i2i−2i00000000000000000−i2i2−i2i2−i2i2−i2i200000000−22−22−22−2200000000
χ592-2-2222-2-22-222-2-2002-22-2-200200000−2i2i−2i2i−2i2i−2i2i00000000000000000i2−i2i2−i2i2−i2i2−i200000000−22−22−22−2200000000
χ602-2-2222-2-22-222-2-2002-22-2-200200000−2i2i−2i2i−2i2i−2i2i00000000000000000−i2i2−i2i2−i2i2−i2i2000000002−22−22−22−200000000
χ612-2-2222-2-22-2-2-222002-2-22200-2000002-22-2-22-2200000000000000000i2−i2i2−i2−i2i2−i2i200000000−i2i2−i2i2i2−i2i2−i200000000
χ622-2-2222-2-22-2-2-222002-2-22200-2000002-22-2-22-2200000000000000000−i2i2−i2i2i2−i2i2−i200000000i2−i2i2−i2−i2i2−i2i200000000
χ632-2-2222-2-22-2-2-222002-2-22200-200000-22-222-22-200000000000000000i2−i2i2−i2−i2i2−i2i200000000i2−i2i2−i2−i2i2−i2i200000000
χ642-2-2222-2-22-2-2-222002-2-22200-200000-22-222-22-200000000000000000−i2i2−i2i2i2−i2i2−i200000000−i2i2−i2i2i2−i2i2−i200000000
χ652-2-22-2-2222-222-2-200-22-22200-2000002i−2i−2i2i2i−2i−2i2i000000000000000002−2−222−2−2200000000−i2i2i2−i2−i2i2i2−i200000000
χ662-2-22-2-2222-222-2-200-22-22200-2000002i−2i−2i2i2i−2i−2i2i00000000000000000−222−2−222−200000000i2−i2−i2i2i2−i2−i2i200000000
χ672-2-22-2-2222-222-2-200-22-22200-200000−2i2i2i−2i−2i2i2i−2i000000000000000002−2−222−2−2200000000i2−i2−i2i2i2−i2−i2i200000000
χ682-2-22-2-2222-222-2-200-22-22200-200000−2i2i2i−2i−2i2i2i−2i00000000000000000−222−2−222−200000000−i2i2i2−i2−i2i2i2−i200000000
χ692-2-22-2-2222-2-2-22200-222-2-2002000002-2-22-222-2000000000000000002−2−22−222−200000000−222−22−2−2200000000
χ702-2-22-2-2222-2-2-22200-222-2-2002000002-2-22-222-200000000000000000−222−22−2−22000000002−2−22−222−200000000
χ712-2-22-2-2222-2-2-22200-222-2-200200000-222-22-2-22000000000000000002−2−22−222−2000000002−2−22−222−200000000
χ722-2-22-2-2222-2-2-22200-222-2-200200000-222-22-2-2200000000000000000−222−22−2−2200000000−222−22−2−2200000000
χ7344-4-44i−4i4i−4i0000004-4000004i−4i00000000000000000004ζ−4ζ4ζ3−4ζ30000000000000000000000000000000000000000
χ7444-4-44i−4i4i−4i0000004-4000004i−4i0000000000000000000−4ζ4ζ−4ζ34ζ30000000000000000000000000000000000000000
χ7544-4-44i−4i4i−4i000000-4400000−4i4i0000000000000004ζ−4ζ4ζ3−4ζ300000000000000000000000000000000000000000000
χ7644-4-44i−4i4i−4i000000-4400000−4i4i000000000000000−4ζ4ζ−4ζ34ζ300000000000000000000000000000000000000000000
χ7744-4-4−4i4i−4i4i0000004-400000−4i4i00000000000000000004ζ3−4ζ34ζ−4ζ0000000000000000000000000000000000000000
χ7844-4-4−4i4i−4i4i0000004-400000−4i4i0000000000000000000−4ζ34ζ3−4ζ4ζ0000000000000000000000000000000000000000
χ7944-4-4−4i4i−4i4i000000-44000004i−4i0000000000000004ζ3−4ζ34ζ−4ζ00000000000000000000000000000000000000000000
χ8044-4-4−4i4i−4i4i000000-44000004i−4i000000000000000−4ζ34ζ3−4ζ4ζ00000000000000000000000000000000000000000000
χ814-4-4444-4-4-444-44-400-444-4400-400000000000000000000000000000000000000000000000000000000000000
χ824-4-4444-4-4-44-44-4400-44-44-400400000000000000000000000000000000000000000000000000000000000000
χ834-4-44-4-444-444-44-4004-4-44-400400000000000000000000000000000000000000000000000000000000000000
χ844-4-44-4-444-44-44-44004-44-4400-400000000000000000000000000000000000000000000000000000000000000
χ858-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ868-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000

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