Finite Group Databasebeta

← Group #227597

Character table — Group #227597

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11111111222222222222222244444444444444444444444444444488888888888888888888161616161616161616161616
order12224444444444448888888824444488888888888888888888888822444488888888888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-11-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111
χ51111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111111111-1-1-1-1-1-111-1-111-1-1-1-1
χ61111111111111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111-1-11111
χ71111111111111111111111111-1-1-1-11-1-1-1-111111111111111111111-11-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-11-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
χ101111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1
χ111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ121111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-111-1-1111111-1-1-1-1-1-1-1-11111-1-111
χ131111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ141111111111111111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-111
χ151111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-111111111-1-11111-1-1-1-111
χ161111111111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111111111-1-1-1-11111-1-1
χ171111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-111-1-11ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-111-1-11-1i−ii−ii−i11-1-1ii−i−i1-11-1i−ii−i1-1i−i
χ181111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-111-1-11ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11-1-11-11−iii−i−ii11-1-1ii−i−i-11-11−ii−ii-11−ii
χ191111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-111-1-11−i−iiiii−i−i−i−i−i−iiiii-1-1-1-1111111-1-11-1i−i−iii−i-1-111ii−i−i1-1-11i−i−ii-11−ii
χ201111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-111-1-11−i−iiiii−i−i−i−i−i−iiiii-1-1-1-111111-1-11-11−ii−ii−ii-1-111ii−i−i-111-1−iii−i1-1i−i
χ211111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1111ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-111-11-1i−ii−ii−i11-1-1−i−iii-111-1−iii−i-11−ii
χ221111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1111ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-1-111-11−iii−i−ii11-1-1−i−iii1-1-11i−i−ii1-1i−i
χ231111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1111−i−iiiii−i−iiiii−i−i−i−i1111-1-1-1-1-111-11-1i−i−iii−i-1-111−i−iii-11-11−ii−ii1-1i−i
χ241111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-1-1111−i−iiiii−i−iiiii−i−i−i−i1111-1-1-1-1-1-111-11−ii−ii−ii-1-111−i−iii1-11-1i−ii−i-11−ii
χ251111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-111-1-11ii−i−i−i−iiiiiii−i−i−i−i-1-1-1-1111111-1-11-1−iii−i−ii-1-111−i−iii1-1-11−iii−i-11i−i
χ261111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-111-1-11ii−i−i−i−iiiiiii−i−i−i−i-1-1-1-111111-1-11-11i−ii−ii−i-1-111−i−iii-111-1i−i−ii1-1−ii
χ271111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-111-1-11−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-111-1-11-1−ii−ii−ii11-1-1−i−iii1-11-1−ii−ii1-1−ii
χ281111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-111-1-11−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11-1-11-11i−i−iii−i11-1-1−i−iii-11-11i−ii−i-11i−i
χ291111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1111ii−i−i−i−iii−i−i−i−iiiii1111-1-1-1-1-111-11-1−iii−i−ii-1-111ii−i−i-11-11i−ii−i1-1−ii
χ301111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1111ii−i−i−i−iii−i−i−i−iiiii1111-1-1-1-1-1-111-11i−ii−ii−i-1-111ii−i−i1-11-1−ii−ii-11i−i
χ311111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1111−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-111-11-1−ii−ii−ii11-1-1ii−i−i-111-1i−i−ii-11i−i
χ321111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-1-1111−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-1-111-11i−i−iii−i11-1-1ii−i−i1-1-11−iii−i1-1−ii
χ332222222222-2-222-2-200000000-22222-22222000022-2-222-2-200000000-20-200000-2-20000000000000000000000
χ342222222222-2-222-2-200000000-22222-2-2-2-2-20000-2-222-2-22200000000-20-200000220000000000000000000000
χ352222222222-2-222-2-200000000-2-2-2-2-2-222220000-2-222-2-2220000000020200000-2-20000000000000000000000
χ362222222222-2-222-2-200000000-2-2-2-2-2-2-2-2-2-2000022-2-222-2-20000000020200000220000000000000000000000
χ3722222222-2-222-2-22222222222-20000-20000-2-2-2-200000000000000000202-2-22200-2-200000000000000000000
χ3822222222-2-222-2-22222222222-20000-20000-2-2-2-200000000000000000-20-222-2-2002200000000000000000000
χ3922222222-2-222-2-222-2-2-2-2-2-2-2-2-20000-20000222200000000000000000202-2-2-2-2002200000000000000000000
χ4022222222-2-222-2-222-2-2-2-2-2-2-2-2-20000-20000222200000000000000000-20-2222200-2-200000000000000000000
χ412222-2-2-2-222-2-2-2-22200000000222-2-2-22i2i−2i−2i00002i2i−2i−2i−2i−2i2i2i00000000-20200000−2i2i0000000000000000000000
χ422222-2-2-2-222-2-2-2-22200000000222-2-2-2−2i−2i2i2i0000−2i−2i2i2i2i2i−2i−2i00000000-202000002i−2i0000000000000000000000
χ432222-2-2-2-222-2-2-2-222000000002-2-222-22i2i−2i−2i0000−2i−2i2i2i2i2i−2i−2i0000000020-200000−2i2i0000000000000000000000
χ442222-2-2-2-222-2-2-2-222000000002-2-222-2−2i−2i2i2i00002i2i−2i−2i−2i−2i2i2i0000000020-2000002i−2i0000000000000000000000
χ452222-2-2-2-2-2-22222-2-22i2i2i2i−2i−2i−2i−2i20000-20000−2i−2i2i2i0000000000000000020-2-222i−2i00−2i2i00000000000000000000
χ462222-2-2-2-2-2-22222-2-22i2i2i2i−2i−2i−2i−2i20000-20000−2i−2i2i2i00000000000000000-2022-2−2i2i002i−2i00000000000000000000
χ472222-2-2-2-2-2-22222-2-2−2i−2i−2i−2i2i2i2i2i20000-200002i2i−2i−2i0000000000000000020-2-22−2i2i002i−2i00000000000000000000
χ482222-2-2-2-2-2-22222-2-2−2i−2i−2i−2i2i2i2i2i20000-200002i2i−2i−2i00000000000000000-2022-22i−2i00−2i2i00000000000000000000
χ492-22-22i−2i2i−2i2-2002i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i02i−2i2-202ζ−2ζ2ζ3−2ζ31+i−1−i1−i−1+i2ζ3−2ζ3002ζ−2ζ00i2i2−i2−i222−2−20000000000002−2i2−i21−i−1+i1+i−1−i000000000000
χ502-22-22i−2i2i−2i2-2002i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i02i−2i2-20−2ζ2ζ−2ζ32ζ31+i−1−i1−i−1+i−2ζ32ζ300−2ζ2ζ00−i2−i2i2i2−2−222000000000000−22−i2i21−i−1+i1+i−1−i000000000000
χ512-22-22i−2i2i−2i2-2002i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i0−2i2i-2202ζ−2ζ2ζ3−2ζ31+i−1−i1−i−1+i−2ζ32ζ300−2ζ2ζ00−i2−i2i2i2−2−2220000000000002−2i2−i2−1+i1−i−1−i1+i000000000000
χ522-22-22i−2i2i−2i2-2002i−2i001+i1+i−1−i−1−i1−i1−i−1+i−1+i0−2i2i-220−2ζ2ζ−2ζ32ζ31+i−1−i1−i−1+i2ζ3−2ζ3002ζ−2ζ00i2i2−i2−i222−2−2000000000000−22−i2i2−1+i1−i−1−i1+i000000000000
χ532-22-22i−2i2i−2i2-2002i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i02i−2i2-202ζ−2ζ2ζ3−2ζ3−1−i1+i−1+i1−i2ζ3−2ζ3002ζ−2ζ00−i2−i2i2i2−2−222000000000000−22−i2i2−1+i1−i−1−i1+i000000000000
χ542-22-22i−2i2i−2i2-2002i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i02i−2i2-20−2ζ2ζ−2ζ32ζ3−1−i1+i−1+i1−i−2ζ32ζ300−2ζ2ζ00i2i2−i2−i222−2−20000000000002−2i2−i2−1+i1−i−1−i1+i000000000000
χ552-22-22i−2i2i−2i2-2002i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i0−2i2i-2202ζ−2ζ2ζ3−2ζ3−1−i1+i−1+i1−i−2ζ32ζ300−2ζ2ζ00i2i2−i2−i222−2−2000000000000−22−i2i21−i−1+i1+i−1−i000000000000
χ562-22-22i−2i2i−2i2-2002i−2i00−1−i−1−i1+i1+i−1+i−1+i1−i1−i0−2i2i-220−2ζ2ζ−2ζ32ζ3−1−i1+i−1+i1−i2ζ3−2ζ3002ζ−2ζ00−i2−i2i2i2−2−2220000000000002−2i2−i21−i−1+i1+i−1−i000000000000
χ572-22-2−2i2i−2i2i2-200−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i02i−2i-2202ζ3−2ζ32ζ−2ζ1−i−1+i1+i−1−i−2ζ2ζ00−2ζ32ζ300−i2−i2i2i222−2−2000000000000−22i2−i2−1−i1+i−1+i1−i000000000000
χ582-22-2−2i2i−2i2i2-200−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i02i−2i-220−2ζ32ζ3−2ζ2ζ1−i−1+i1+i−1−i2ζ−2ζ002ζ3−2ζ300i2i2−i2−i2−2−2220000000000002−2−i2i2−1−i1+i−1+i1−i000000000000
χ592-22-2−2i2i−2i2i2-200−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i0−2i2i2-202ζ3−2ζ32ζ−2ζ1−i−1+i1+i−1−i2ζ−2ζ002ζ3−2ζ300i2i2−i2−i2−2−222000000000000−22i2−i21+i−1−i1−i−1+i000000000000
χ602-22-2−2i2i−2i2i2-200−2i2i001−i1−i−1+i−1+i1+i1+i−1−i−1−i0−2i2i2-20−2ζ32ζ3−2ζ2ζ1−i−1+i1+i−1−i−2ζ2ζ00−2ζ32ζ300−i2−i2i2i222−2−20000000000002−2−i2i21+i−1−i1−i−1+i000000000000
χ612-22-2−2i2i−2i2i2-200−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i02i−2i-2202ζ3−2ζ32ζ−2ζ−1+i1−i−1−i1+i−2ζ2ζ00−2ζ32ζ300i2i2−i2−i2−2−2220000000000002−2−i2i21+i−1−i1−i−1+i000000000000
χ622-22-2−2i2i−2i2i2-200−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i02i−2i-220−2ζ32ζ3−2ζ2ζ−1+i1−i−1−i1+i2ζ−2ζ002ζ3−2ζ300−i2−i2i2i222−2−2000000000000−22i2−i21+i−1−i1−i−1+i000000000000
χ632-22-2−2i2i−2i2i2-200−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i0−2i2i2-202ζ3−2ζ32ζ−2ζ−1+i1−i−1−i1+i2ζ−2ζ002ζ3−2ζ300−i2−i2i2i222−2−20000000000002−2−i2i2−1−i1+i−1+i1−i000000000000
χ642-22-2−2i2i−2i2i2-200−2i2i00−1+i−1+i1−i1−i−1−i−1−i1+i1+i0−2i2i2-20−2ζ32ζ3−2ζ2ζ−1+i1−i−1−i1+i−2ζ2ζ00−2ζ32ζ300i2i2−i2−i2−2−222000000000000−22i2−i2−1−i1+i−1+i1−i000000000000
χ6544444444-4-4-4-4-4-4-4-40000000040000400000000000000000000000000000000000000000000000000000000
χ664444-4-4-4-4-4-4-4-4444400000000-40000400000000000000000000000000000000000000000000000000000000
χ6744-4-444-4-40000000022−2222−2222−2222−22000000000000000022−220022−222-22-22-22-200000000000000000000000000000000
χ6844-4-444-4-40000000022−2222−2222−2222−220000000000000000−222200−2222-22-22-22-2200000000000000000000000000000000
χ6944-4-444-4-400000000−2222−2222−2222−2222000000000000000022−220022−22-22-22-22-2200000000000000000000000000000000
χ7044-4-444-4-400000000−2222−2222−2222−22220000000000000000−222200−22222-22-22-22-200000000000000000000000000000000
χ7144-4-4-4-444000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000002i2−2i200−2i22i22-22-2-22-2200000000000000000000000000000000
χ7244-4-4-4-444000000002i2−2i22i2−2i2−2i22i2−2i22i20000000000000000−2i22i2002i2−2i2-22-222-22-200000000000000000000000000000000
χ7344-4-4-4-44400000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000002i2−2i200−2i22i2-22-222-22-200000000000000000000000000000000
χ7444-4-4-4-44400000000−2i22i2−2i22i22i2−2i22i2−2i20000000000000000−2i22i2002i2−2i22-22-2-22-2200000000000000000000000000000000
χ754-44-44i−4i4i−4i-4400−4i4i002+2i2+2i−2−2i−2−2i2−2i2−2i−2+2i−2+2i0000000000−2−2i2+2i−2+2i2−2i000000000000000000000000000000000000000000000000
χ764-44-44i−4i4i−4i-4400−4i4i00−2−2i−2−2i2+2i2+2i−2+2i−2+2i2−2i2−2i00000000002+2i−2−2i2−2i−2+2i000000000000000000000000000000000000000000000000
χ774-44-4−4i4i−4i4i-44004i−4i002−2i2−2i−2+2i−2+2i2+2i2+2i−2−2i−2−2i0000000000−2+2i2−2i−2−2i2+2i000000000000000000000000000000000000000000000000
χ784-44-4−4i4i−4i4i-44004i−4i00−2+2i−2+2i2−2i2−2i−2−2i−2−2i2+2i2+2i00000000002−2i−2+2i2+2i−2−2i000000000000000000000000000000000000000000000000
χ794-4-444i−4i−4i4i004-4004i−4i0000000000000000000000000000002i2−2i2−2i22i222−22−222200000000000000000000000000000000
χ804-4-444i−4i−4i4i004-4004i−4i000000000000000000000000000000−2i22i22i2−2i2−222222−2200000000000000000000000000000000
χ814-4-444i−4i−4i4i00-4400−4i4i4ζ−4ζ−4ζ4ζ−4ζ34ζ34ζ3−4ζ300000000000000000000000000000000000000000000000000000000000000
χ824-4-444i−4i−4i4i00-4400−4i4i−4ζ4ζ4ζ−4ζ4ζ3−4ζ3−4ζ34ζ300000000000000000000000000000000000000000000000000000000000000
χ834-4-44−4i4i4i−4i004-400−4i4i0000000000000000000000000000002i2−2i2−2i22i2−222222−2200000000000000000000000000000000
χ844-4-44−4i4i4i−4i004-400−4i4i000000000000000000000000000000−2i22i22i2−2i222−22−222200000000000000000000000000000000
χ854-4-44−4i4i4i−4i00-44004i−4i4ζ3−4ζ3−4ζ34ζ3−4ζ4ζ4ζ−4ζ00000000000000000000000000000000000000000000000000000000000000
χ864-4-44−4i4i4i−4i00-44004i−4i−4ζ34ζ34ζ3−4ζ34ζ−4ζ−4ζ4ζ00000000000000000000000000000000000000000000000000000000000000

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