Finite Group Databasebeta

← Group #210341

Character table — Group #210341

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size1111111122222222222222224444444444444444444444888888888888888888888888888888881616161616161616
order12224444224444448888888822224444448888888888882224444488888888888888888888888844448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-11111111111-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111-1-111-1-11111111111-1-1-1-11-1-1-1-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ5111111111111111111111111-1-111-1-111111111-1-1-1-11111-1-1-111-1-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-111111111-1-1-1-11111-1-1-111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-111
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1
χ111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111-1-1-1-11-1-111-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ121111111111111111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111111-1-1-1-11-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ131111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ141111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ171111-1-1-1-1-1-1111-1-11iiii−i−i−i−i1111-1-1-1-11-1ii−i−iii−i−iii−i−i-1111-11-1-1i−ii−iii−i−i11-1-1ii−i−i11-1-1ii−i−i1-1i−ii−i1-1
χ181111-1-1-1-1-1-1111-1-11iiii−i−i−i−i1111-1-1-1-11-1ii−i−iii−i−iii−i−i-1111-11-1-1i−ii−iii−i−i-1-111−i−iii-1-111−i−iii-11−ii−ii-11
χ191111-1-1-1-1-1-1111-1-11iiii−i−i−i−i11-1-1-1-1111-1ii−i−iii−i−i−i−iii-1-1-1-11111−iii−i−i−iii11-1-1ii−i−i-1-111−i−iii1-1−iii−i-11
χ201111-1-1-1-1-1-1111-1-11iiii−i−i−i−i11-1-1-1-1111-1ii−i−iii−i−i−i−iii-1-1-1-11111−iii−i−i−iii-1-111−i−iii11-1-1ii−i−i-11i−i−ii1-1
χ211111-1-1-1-1-1-1111-1-11iiii−i−i−i−i-1-11111-1-11-1ii−i−i−i−iiiii−i−i1-1-11-1-111i−i−ii−i−iii11-1-1ii−i−i11-1-1ii−i−i-11−ii−ii-11
χ221111-1-1-1-1-1-1111-1-11iiii−i−i−i−i-1-11111-1-11-1ii−i−i−i−iiiii−i−i1-1-11-1-111i−i−ii−i−iii-1-111−i−iii-1-111−i−iii1-1i−ii−i1-1
χ231111-1-1-1-1-1-1111-1-11iiii−i−i−i−i-1-1-1-111111-1ii−i−i−i−iii−i−iii111-11-1-1-1−ii−iiii−i−i11-1-1ii−i−i-1-111−i−iii-11i−i−ii1-1
χ241111-1-1-1-1-1-1111-1-11iiii−i−i−i−i-1-1-1-111111-1ii−i−i−i−iii−i−iii111-11-1-1-1−ii−iiii−i−i-1-111−i−iii11-1-1ii−i−i1-1−iii−i-11
χ251111-1-1-1-1-1-1111-1-11−i−i−i−iiiii1111-1-1-1-11-1−i−iii−i−iii−i−iii-1111-11-1-1−ii−ii−i−iii11-1-1−i−iii11-1-1−i−iii1-1−ii−ii1-1
χ261111-1-1-1-1-1-1111-1-11−i−i−i−iiiii1111-1-1-1-11-1−i−iii−i−iii−i−iii-1111-11-1-1−ii−ii−i−iii-1-111ii−i−i-1-111ii−i−i-11i−ii−i-11
χ271111-1-1-1-1-1-1111-1-11−i−i−i−iiiii11-1-1-1-1111-1−i−iii−i−iiiii−i−i-1-1-1-11111i−i−iiii−i−i11-1-1−i−iii-1-111ii−i−i1-1i−i−ii-11
χ281111-1-1-1-1-1-1111-1-11−i−i−i−iiiii11-1-1-1-1111-1−i−iii−i−iiiii−i−i-1-1-1-11111i−i−iiii−i−i-1-111ii−i−i11-1-1−i−iii-11−iii−i1-1
χ291111-1-1-1-1-1-1111-1-11−i−i−i−iiiii-1-11111-1-11-1−i−iiiii−i−i−i−iii1-1-11-1-111−iii−iii−i−i11-1-1−i−iii11-1-1−i−iii-11i−ii−i-11
χ301111-1-1-1-1-1-1111-1-11−i−i−i−iiiii-1-11111-1-11-1−i−iiiii−i−i−i−iii1-1-11-1-111−iii−iii−i−i-1-111ii−i−i-1-111ii−i−i1-1−ii−ii1-1
χ311111-1-1-1-1-1-1111-1-11−i−i−i−iiiii-1-1-1-111111-1−i−iiiii−i−iii−i−i111-11-1-1-1i−ii−i−i−iii11-1-1−i−iii-1-111ii−i−i-11−iii−i1-1
χ321111-1-1-1-1-1-1111-1-11−i−i−i−iiiii-1-1-1-111111-1−i−iiiii−i−iii−i−i111-11-1-1-1i−ii−i−i−iii-1-111ii−i−i11-1-1−i−iii1-1i−i−ii-11
χ3322222222222-2-2-2-222222222200220022-2-2-2-2-2-200002222000-2-2000-2-2000000000000000000000000000000
χ3422222222222-2-2-2-222222222200-2-200-2-2-2-2-2-2-2-20000-2-2-2-20002200022000000000000000000000000000000
χ3522222222222-2-2-2-22-2-2-2-2-2-2-2-200220022-2-222220000-2-2-2-2000-2-200022000000000000000000000000000000
χ3622222222222-2-2-2-22-2-2-2-2-2-2-2-200-2-200-2-2-2-222220000222200022000-2-2000000000000000000000000000000
χ3722222222-2-2-22222-222-2-222-2-222002200-2-22-22-222220000-20000-20000-2-20000000000000000000000000000
χ3822222222-2-2-22222-222-2-222-2-2-2-200-2-200-2-22-22-2-2-2-2-200002000020000220000000000000000000000000000
χ3922222222-2-2-22222-2-2-222-2-22222002200-2-2-22-22-2-2-2-20000-20000-20000220000000000000000000000000000
χ4022222222-2-2-22222-2-2-222-2-222-2-200-2-200-2-2-22-22222200002000020000-2-20000000000000000000000000000
χ4122222222-2-2-2-2-2-2-2-222-2-222-2-20000000022-22-220000000002-20002-200002-22-2000000000000000000000000
χ4222222222-2-2-2-2-2-2-2-222-2-222-2-20000000022-22-22000000000-22000-220000-22-22000000000000000000000000
χ4322222222-2-2-2-2-2-2-2-2-2-222-2-22200000000222-22-20000000002-20002-20000-22-22000000000000000000000000
χ4422222222-2-2-2-2-2-2-2-2-2-222-2-22200000000222-22-2000000000-22000-2200002-22-2000000000000000000000000
χ452222-2-2-2-222-222-2-2-22i2i−2i−2i−2i−2i2i2i2200-2-200-222i−2i−2i2i2i2i−2i−2i000020000-20000−2i2i0000000000000000000000000000
χ462222-2-2-2-222-222-2-2-22i2i−2i−2i−2i−2i2i2i-2-2002200-222i−2i−2i2i−2i−2i2i2i0000-20000200002i−2i0000000000000000000000000000
χ472222-2-2-2-222-222-2-2-2−2i−2i2i2i2i2i−2i−2i2200-2-200-22−2i2i2i−2i−2i−2i2i2i000020000-200002i−2i0000000000000000000000000000
χ482222-2-2-2-222-222-2-2-2−2i−2i2i2i2i2i−2i−2i-2-2002200-22−2i2i2i−2i2i2i−2i−2i0000-2000020000−2i2i0000000000000000000000000000
χ492222-2-2-2-222-2-2-222-22i2i−2i−2i−2i−2i2i2i000000002-2−2i2i2i−2i0000000002-2000-2200002i−2i−2i2i000000000000000000000000
χ502222-2-2-2-222-2-2-222-22i2i−2i−2i−2i−2i2i2i000000002-2−2i2i2i−2i000000000-220002-20000−2i2i2i−2i000000000000000000000000
χ512222-2-2-2-222-2-2-222-2−2i−2i2i2i2i2i−2i−2i000000002-22i−2i−2i2i0000000002-2000-220000−2i2i2i−2i000000000000000000000000
χ522222-2-2-2-222-2-2-222-2−2i−2i2i2i2i2i−2i−2i000000002-22i−2i−2i2i000000000-220002-200002i−2i−2i2i000000000000000000000000
χ532222-2-2-2-2-2-22-2-22222i2i2i2i−2i−2i−2i−2i002200-2-2-22−2i−2i2i2i00002i2i−2i−2i000-22000−2i2i000000000000000000000000000000
χ542222-2-2-2-2-2-22-2-22222i2i2i2i−2i−2i−2i−2i00-2-20022-22−2i−2i2i2i0000−2i−2i2i2i0002-20002i−2i000000000000000000000000000000
χ552222-2-2-2-2-2-22-2-2222−2i−2i−2i−2i2i2i2i2i002200-2-2-222i2i−2i−2i0000−2i−2i2i2i000-220002i−2i000000000000000000000000000000
χ562222-2-2-2-2-2-22-2-2222−2i−2i−2i−2i2i2i2i2i00-2-20022-222i2i−2i−2i00002i2i−2i−2i0002-2000−2i2i000000000000000000000000000000
χ572-2-2222-2-2-2220000-22i−2i2i−2i2i−2i2i−2i002-2002-200000000002i−2i2i−2i0000000000000000i2−i2i2−i22−22−2i2−i2i2−i22−22−200000000
χ582-2-2222-2-2-2220000-22i−2i2i−2i2i−2i2i−2i002-2002-200000000002i−2i2i−2i0000000000000000−i2i2−i2i2−22−22−i2i2−i2i2−22−2200000000
χ592-2-2222-2-2-2220000-22i−2i2i−2i2i−2i2i−2i00-2200-220000000000−2i2i−2i2i0000000000000000i2−i2i2−i22−22−2−i2i2−i2i2−22−2200000000
χ602-2-2222-2-2-2220000-22i−2i2i−2i2i−2i2i−2i00-2200-220000000000−2i2i−2i2i0000000000000000−i2i2−i2i2−22−22i2−i2i2−i22−22−200000000
χ612-2-2222-2-2-2220000-2−2i2i−2i2i−2i2i−2i2i002-2002-20000000000−2i2i−2i2i0000000000000000i2−i2i2−i2−22−22i2−i2i2−i2−22−2200000000
χ622-2-2222-2-2-2220000-2−2i2i−2i2i−2i2i−2i2i002-2002-20000000000−2i2i−2i2i0000000000000000−i2i2−i2i22−22−2−i2i2−i2i22−22−200000000
χ632-2-2222-2-2-2220000-2−2i2i−2i2i−2i2i−2i2i00-2200-2200000000002i−2i2i−2i0000000000000000i2−i2i2−i2−22−22−i2i2−i2i22−22−200000000
χ642-2-2222-2-2-2220000-2−2i2i−2i2i−2i2i−2i2i00-2200-2200000000002i−2i2i−2i0000000000000000−i2i2−i2i22−22−2i2−i2i2−i2−22−2200000000
χ652-2-22-2-2222-220000-22-22-2-22-22002-200-2200000000002-2-220000000000000000i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i200000000
χ662-2-22-2-2222-220000-22-22-2-22-22002-200-2200000000002-2-220000000000000000−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i200000000
χ672-2-22-2-2222-220000-22-22-2-22-2200-22002-20000000000-222-20000000000000000i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i200000000
χ682-2-22-2-2222-220000-22-22-2-22-2200-22002-20000000000-222-20000000000000000−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i200000000
χ692-2-22-2-2222-220000-2-22-222-22-2002-200-220000000000-222-20000000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i200000000
χ702-2-22-2-2222-220000-2-22-222-22-2002-200-220000000000-222-20000000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i200000000
χ712-2-22-2-2222-220000-2-22-222-22-200-22002-200000000002-2-220000000000000000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i200000000
χ722-2-22-2-2222-220000-2-22-222-22-200-22002-200000000002-2-220000000000000000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i200000000
χ7344-4-44i−4i4i−4i0004-44i−4i000000000000000000000004ζ−4ζ4ζ3−4ζ300000000000000000000000000000000000000000000
χ7444-4-44i−4i4i−4i0004-44i−4i00000000000000000000000−4ζ4ζ−4ζ34ζ300000000000000000000000000000000000000000000
χ7544-4-44i−4i4i−4i000-44−4i4i0000000004-4004i−4i00000000000000000000000000000000000000000000000000000000
χ7644-4-44i−4i4i−4i000-44−4i4i000000000-4400−4i4i00000000000000000000000000000000000000000000000000000000
χ7744-4-4−4i4i−4i4i0004-4−4i4i000000000000000000000004ζ3−4ζ34ζ−4ζ00000000000000000000000000000000000000000000
χ7844-4-4−4i4i−4i4i0004-4−4i4i00000000000000000000000−4ζ34ζ3−4ζ4ζ00000000000000000000000000000000000000000000
χ7944-4-4−4i4i−4i4i000-444i−4i0000000004-400−4i4i00000000000000000000000000000000000000000000000000000000
χ8044-4-4−4i4i−4i4i000-444i−4i000000000-44004i−4i00000000000000000000000000000000000000000000000000000000
χ814-4-4444-4-44-4-4000044i−4i−4i4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000
χ824-4-4444-4-44-4-400004−4i4i4i−4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000
χ834-4-44-4-444-44-4000044-4-44-444-400000000000000000000000000000000000000000000000000000000000000
χ844-4-44-4-444-44-400004-444-44-4-4400000000000000000000000000000000000000000000000000000000000000
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.