Finite Group Databasebeta

← Group #140306

Character table — Group #140306

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122244442244444444444444888888884444448888888888888888888888888888161616161616161616161616161616164488
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1
χ61111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111
χ71111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111
χ81111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1
χ91111-1-1-1-1-1-11-1-1iiii−i−i−i−i1111111-1-1-1-11ii−i−i-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-11-1i−i
χ101111-1-1-1-1-1-11-1-1iiii−i−i−i−i1111111-1-1-1-11ii−i−i-111-1-1iiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-11−ii
χ111111-1-1-1-1-1-11-1-1iiii−i−i−i−i1111111-1-1-1-11ii−i−i-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1-11−ii
χ121111-1-1-1-1-1-11-1-1iiii−i−i−i−i1111111-1-1-1-11ii−i−i-111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiii-1-1-1-111111-1i−i
χ131111-1-1-1-1-1-11-1-1−i−i−i−iiiii1111111-1-1-1-11−i−iii-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-111111-1−ii
χ141111-1-1-1-1-1-11-1-1−i−i−i−iiiii1111111-1-1-1-11−i−iii-111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1-11i−i
χ151111-1-1-1-1-1-11-1-1−i−i−i−iiiii1111111-1-1-1-11−i−iii-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-11i−i
χ161111-1-1-1-1-1-11-1-1−i−i−i−iiiii1111111-1-1-1-11−i−iii-111-1-1−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-11-1−ii
χ17222222222222222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-2222-2-2-2-2-2-2-2-22-2-2-2-22-2-2-2-222222222000000000000000000000000000000000000
χ1922222222222-2-222222222-2-2200000000-2-2-2-2-2-2000000000000000000000000000022−2−222−2−222−2−222−2−20000
χ2022222222222-2-222222222-2-2200000000-2-2-2-2-2-20000000000000000000000000000−2−222−2−222−2−222−2−2220000
χ2122222222222-2-2-2-2-2-2-2-2-2-2-2-2200000000-22222-2000000000000000000000000000022−2−222−2−2−2−222−2−2220000
χ2222222222222-2-2-2-2-2-2-2-2-2-2-2-2200000000-22222-20000000000000000000000000000−2−222−2−22222−2−222−2−20000
χ2322222222-2-2-2220000000022-222222222-20000-2-2-2-2-20000000022-2-222-2-20000000000000000000000000000
χ2422222222-2-2-2220000000022-222222222-20000-2-2-2-2-200000000-2-222-2-2220000000000000000000000000000
χ2522222222-2-2-2220000000022-2-2-2-2-2-2-2-2-2-20000-2222200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2622222222-2-2-2220000000022-2-2-2-2-2-2-2-2-2-20000-222220000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ272222-2-2-2-222-2-2-20000000022-22222-2-2-2-2-200002-2-222000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ282222-2-2-2-222-2-2-20000000022-22222-2-2-2-2-200002-2-22200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ292222-2-2-2-222-2-2-20000000022-2-2-2-2-22222-20000222-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ302222-2-2-2-222-2-2-20000000022-2-2-2-2-22222-20000222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ312222-2-2-2-2-2-22222i2i2i2i−2i−2i−2i−2i-2-2200000000-2−2i−2i2i2i20000000000000000000000000000i2i2−i2−i2−i2−i2i2i222−2−2−2−2220000
χ322222-2-2-2-2-2-22222i2i2i2i−2i−2i−2i−2i-2-2200000000-2−2i−2i2i2i20000000000000000000000000000−i2−i2i2i2i2i2−i2−i2−2−22222−2−20000
χ332222-2-2-2-2-2-2222−2i−2i−2i−2i2i2i2i2i-2-2200000000-22i2i−2i−2i20000000000000000000000000000i2i2−i2−i2−i2−i2i2i2−2−22222−2−20000
χ342222-2-2-2-2-2-2222−2i−2i−2i−2i2i2i2i2i-2-2200000000-22i2i−2i−2i20000000000000000000000000000−i2−i2i2i2i2i2−i2−i222−2−2−2−2220000
χ352222-2-2-2-2-2-22-2-22i2i2i2i−2i−2i−2i−2i222-2-2-2-2222222i2i−2i−2i-2-2-222−2i−2i−2i−2i2i2i2i2i000000000000000000000000000000000000
χ362222-2-2-2-2-2-22-2-2−2i−2i−2i−2i2i2i2i2i222-2-2-2-222222−2i−2i2i2i-2-2-2222i2i2i2i−2i−2i−2i−2i000000000000000000000000000000000000
χ3722-2-222-2-22-220022-2-222-2-200-222−2−222−2−20000002−22−222−2−222−2−20000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ3822-2-222-2-22-220022-2-222-2-200-222−2−222−2−20000002−22−222−2−222−2−20000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ3922-2-222-2-22-220022-2-222-2-200-2−2−222−2−222000000−22−22−2−222−2−2220000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ4022-2-222-2-22-220022-2-222-2-200-2−2−222−2−222000000−22−22−2−222−2−2220000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ4122-2-222-2-22-2200-2-222-2-22200-222−2−222−2−20000002−22−2−2−222−2−2220000000000000000ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ4222-2-222-2-22-2200-2-222-2-22200-222−2−222−2−20000002−22−2−2−222−2−2220000000000000000−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ4322-2-222-2-22-2200-2-222-2-22200-2−2−222−2−222000000−22−2222−2−222−2−20000000000000000ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ4422-2-222-2-22-2200-2-222-2-22200-2−2−222−2−222000000−22−2222−2−222−2−20000000000000000−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ4522-2-2-2-222-222002i2i−2i−2i−2i−2i2i2i00-222−2−2−2−2220000002−2−22i2i2−i2−i2−i2−i2i2i20000000000000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ4622-2-2-2-222-222002i2i−2i−2i−2i−2i2i2i00-222−2−2−2−2220000002−2−22i2i2−i2−i2−i2−i2i2i20000000000000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ4722-2-2-2-222-222002i2i−2i−2i−2i−2i2i2i00-2−2−22222−2−2000000−222−2−i2−i2i2i2i2i2−i2−i20000000000000000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ4822-2-2-2-222-222002i2i−2i−2i−2i−2i2i2i00-2−2−22222−2−2000000−222−2−i2−i2i2i2i2i2−i2−i20000000000000000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ4922-2-2-2-222-22200−2i−2i2i2i2i2i−2i−2i00-222−2−2−2−2220000002−2−22−i2−i2i2i2i2i2−i2−i20000000000000000ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ50000
χ5022-2-2-2-222-22200−2i−2i2i2i2i2i−2i−2i00-222−2−2−2−2220000002−2−22−i2−i2i2i2i2i2−i2−i20000000000000000−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ50000
χ5122-2-2-2-222-22200−2i−2i2i2i2i2i−2i−2i00-2−2−22222−2−2000000−222−2i2i2−i2−i2−i2−i2i2i20000000000000000ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ70000
χ5222-2-2-2-222-22200−2i−2i2i2i2i2i−2i−2i00-2−2−22222−2−2000000−222−2i2i2−i2−i2−i2−i2i2i20000000000000000−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ70000
χ532-22-22i−2i2i−2i0002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i2-202-22-22i−2i2i−2i01+i−1−i1−i−1+i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ6−2ζ6002ζ2−2ζ2i2−i2i2−i22−22−200000000000000000000
χ542-22-22i−2i2i−2i0002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i2-202-22-22i−2i2i−2i01+i−1−i1−i−1+i000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ62ζ600−2ζ22ζ2−i2i2−i2i2−22−2200000000000000000000
χ552-22-22i−2i2i−2i0002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i2-20-22-22−2i2i−2i2i01+i−1−i1−i−1+i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i2ζ2−2ζ2002ζ6−2ζ6002−2−22−i2i2i2−i200000000000000000000
χ562-22-22i−2i2i−2i0002i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i2-20-22-22−2i2i−2i2i01+i−1−i1−i−1+i00000−1−i1+i−1−i1+i−1+i1−i−1+i1−i−2ζ22ζ200−2ζ62ζ600−222−2i2−i2−i2i200000000000000000000
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χ642-22-2−2i2i−2i2i000−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i2-20-22-222i−2i2i−2i01−i−1+i1+i−1−i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−2ζ62ζ600−2ζ22ζ2002−2−22i2−i2−i2i200000000000000000000
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χ662-22-2−2i2i−2i2i000−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i2-202-22-2−2i2i−2i2i0−1+i1−i−1−i1+i00000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ22ζ200−2ζ62ζ6i2−i2i2−i2−22−2200000000000000000000
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χ6944444444-4-4-4-4-400000000-4-4-400000000400004000000000000000000000000000000000000000000000000
χ704444-4-4-4-444-44400000000-4-4-40000000040000-4000000000000000000000000000000000000000000000000
χ7144-4-444-4-4-44-400000000000042222−22−222222−22−22000000−2222−222200000000000000000000000000000000000000000000
χ7244-4-444-4-4-44-40000000000004−22−222222−22−22222200000022−2222−2200000000000000000000000000000000000000000000
χ7344-4-4-4-4444-4-400000000000042222−22−22−22−222222000000−222222−2200000000000000000000000000000000000000000000
χ7444-4-4-4-4444-4-40000000000004−22−2222222222−22−2200000022−22−222200000000000000000000000000000000000000000000
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χ784-44-4−4i4i−4i4i0004i−4i−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i-4400000000002−2i−2+2i2+2i−2−2i0000000000000000000000000000000000000000000000000
χ794-4-444i−4i−4i4i000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i00022−22−22222i2−2i2−2i22i200000000002ζ2−2ζ2−2ζ22ζ2−2ζ62ζ62ζ6−2ζ6000000000000000000000000000000000000
χ804-4-444i−4i−4i4i000002+2i−2−2i−2−2i2+2i2−2i−2+2i−2+2i2−2i000−222222−22−2i22i22i2−2i20000000000−2ζ22ζ22ζ2−2ζ22ζ6−2ζ6−2ζ62ζ6000000000000000000000000000000000000
χ814-4-444i−4i−4i4i00000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i00022−22−22222i2−2i2−2i22i20000000000−2ζ22ζ22ζ2−2ζ22ζ6−2ζ6−2ζ62ζ6000000000000000000000000000000000000
χ824-4-444i−4i−4i4i00000−2−2i2+2i2+2i−2−2i−2+2i2−2i2−2i−2+2i000−222222−22−2i22i22i2−2i200000000002ζ2−2ζ2−2ζ22ζ2−2ζ62ζ62ζ6−2ζ6000000000000000000000000000000000000
χ834-4-44−4i4i4i−4i000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i00022−22−2222−2i22i22i2−2i20000000000−2ζ62ζ62ζ6−2ζ62ζ2−2ζ2−2ζ22ζ2000000000000000000000000000000000000
χ844-4-44−4i4i4i−4i000002−2i−2+2i−2+2i2−2i2+2i−2−2i−2−2i2+2i000−222222−222i2−2i2−2i22i200000000002ζ6−2ζ6−2ζ62ζ6−2ζ22ζ22ζ2−2ζ2000000000000000000000000000000000000
χ854-4-44−4i4i4i−4i00000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i00022−22−2222−2i22i22i2−2i200000000002ζ6−2ζ6−2ζ62ζ6−2ζ22ζ22ζ2−2ζ2000000000000000000000000000000000000
χ864-4-44−4i4i4i−4i00000−2+2i2−2i2−2i−2+2i−2−2i2+2i2+2i−2−2i000−222222−222i2−2i2−2i22i20000000000−2ζ62ζ62ζ6−2ζ62ζ2−2ζ2−2ζ22ζ2000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.