Finite Group Databasebeta

← Group #141322

Character table — Group #141322

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111111112222222222222222222222224444444444444444448888888888888888888888888888888832323232
order122244442244444488888888888888884488888888888888884444444488888888161616161616161616161616161616162244
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
χ511111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1
χ611111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-11-11
χ711111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-11-11
χ811111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111-11-1
χ91111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-1
χ101111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111
χ111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111
χ121111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-1
χ131111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11
χ141111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-111-1
χ151111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-1
χ161111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11
χ172222222222222222-2-2-2-222222222-2-2-2-222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222000000000000000000000000000000000000
χ192222222222-2-2-2-2220000222222220000-2-20000-2-2-2-200000000000000000000000022−2−222−2−222−2−222−2−20000
χ202222222222-2-2-2-2220000222222220000-2-20000-2-2-2-2000000000000000000000000−2−222−2−222−2−222−2−2220000
χ212222222222-2-2-2-2220000-2-2-2-2-2-2-2-20000-2-20000222200000000000000000000000022−2−222−2−2−2−222−2−2220000
χ222222222222-2-2-2-2220000-2-2-2-2-2-2-2-20000-2-200002222000000000000000000000000−2−222−2−22222−2−222−2−20000
χ2322222222-2-22222-2-22222000000002222-2-2-2-2-2-20000000000000000000022-2-222-2-200000000000000000000
χ2422222222-2-22222-2-22222000000002222-2-2-2-2-2-200000000000000000000-2-222-2-22200000000000000000000
χ2522222222-2-22222-2-2-2-2-2-200000000-2-2-2-2-2-222220000000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ2622222222-2-22222-2-2-2-2-2-200000000-2-2-2-2-2-22222000000000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ272222-2-2-2-222-2-222-2-2222200000000-2-2-2-22-2-2-222000000000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ282222-2-2-2-222-2-222-2-2222200000000-2-2-2-22-2-2-22200000000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ292222-2-2-2-222-2-222-2-2-2-2-2-20000000022222-222-2-200000000000022-2-2-2-2220000000000000000000000000000
χ302222-2-2-2-222-2-222-2-2-2-2-2-20000000022222-222-2-2000000000000-2-22222-2-20000000000000000000000000000
χ312222-2-2-2-2-2-222-2-22200002222-2-2-2-200002-20000-2-222000000000000000000000000i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i20000
χ322222-2-2-2-2-2-222-2-22200002222-2-2-2-200002-20000-2-222000000000000000000000000−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i20000
χ332222-2-2-2-2-2-222-2-2220000-2-2-2-2222200002-2000022-2-2000000000000000000000000i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i20000
χ342222-2-2-2-2-2-222-2-2220000-2-2-2-2222200002-2000022-2-2000000000000000000000000−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i20000
χ352222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-22222-22-2-22222-2-2-2-2-2-22222000000000000000000000000000000000000
χ362222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222222222-22-2-222-2-2222222-2-2-2-2000000000000000000000000000000000000
χ3722-2-22i−2i2i−2i002i−2i2-20022-2-222−2−2i2i2−i2−i22i2i−2i−2i0000002−2i2−i222−2−2i2i2−i2−i21+i−1−i1+i−1−i1−i−1+i1−i−1+i002ζ2−2ζ2002ζ6−2ζ600000000000000000000
χ3822-2-22i−2i2i−2i002i−2i2-20022-2-222−2−2i2i2−i2−i22i2i−2i−2i0000002−2i2−i222−2−2i2i2−i2−i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i00−2ζ22ζ200−2ζ62ζ600000000000000000000
χ3922-2-22i−2i2i−2i002i−2i2-20022-2-2−2−222−i2−i2i2i22i2i−2i−2i000000−22−i2i2−2−222−i2−i2i2i21+i−1−i1+i−1−i1−i−1+i1−i−1+i00−2ζ22ζ200−2ζ62ζ600000000000000000000
χ4022-2-22i−2i2i−2i002i−2i2-20022-2-2−2−222−i2−i2i2i22i2i−2i−2i000000−22−i2i2−2−222−i2−i2i2i2−1−i1+i−1−i1+i−1+i1−i−1+i1−i002ζ2−2ζ2002ζ6−2ζ600000000000000000000
χ4122-2-22i−2i2i−2i002i−2i2-200-2-22222−2−2i2i2−i2−i2−2i−2i2i2i0000002−2i2−i2−2−222−i2−i2i2i21−i−1+i−1+i1−i−1−i1+i1+i−1−i2ζ6−2ζ6002ζ2−2ζ20000000000000000000000
χ4222-2-22i−2i2i−2i002i−2i2-200-2-22222−2−2i2i2−i2−i2−2i−2i2i2i0000002−2i2−i2−2−222−i2−i2i2i2−1+i1−i1−i−1+i1+i−1−i−1−i1+i−2ζ62ζ600−2ζ22ζ20000000000000000000000
χ4322-2-22i−2i2i−2i002i−2i2-200-2-222−2−222−i2−i2i2i2−2i−2i2i2i000000−22−i2i222−2−2i2i2−i2−i21−i−1+i−1+i1−i−1−i1+i1+i−1−i−2ζ62ζ600−2ζ22ζ20000000000000000000000
χ4422-2-22i−2i2i−2i002i−2i2-200-2-222−2−222−i2−i2i2i2−2i−2i2i2i000000−22−i2i222−2−2i2i2−i2−i2−1+i1−i1−i−1+i1+i−1−i−1−i1+i2ζ6−2ζ6002ζ2−2ζ20000000000000000000000
χ4522-2-2−2i2i−2i2i00−2i2i2-20022-2-222−2−2−i2−i2i2i2−2i−2i2i2i0000002−2−i2i222−2−2−i2−i2i2i21−i−1+i1−i−1+i1+i−1−i1+i−1−i00−2ζ62ζ600−2ζ22ζ200000000000000000000
χ4622-2-2−2i2i−2i2i00−2i2i2-20022-2-222−2−2−i2−i2i2i2−2i−2i2i2i0000002−2−i2i222−2−2−i2−i2i2i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i002ζ6−2ζ6002ζ2−2ζ200000000000000000000
χ4722-2-2−2i2i−2i2i00−2i2i2-20022-2-2−2−222i2i2−i2−i2−2i−2i2i2i000000−22i2−i2−2−222i2i2−i2−i21−i−1+i1−i−1+i1+i−1−i1+i−1−i002ζ6−2ζ6002ζ2−2ζ200000000000000000000
χ4822-2-2−2i2i−2i2i00−2i2i2-20022-2-2−2−222i2i2−i2−i2−2i−2i2i2i000000−22i2−i2−2−222i2i2−i2−i2−1+i1−i−1+i1−i−1−i1+i−1−i1+i00−2ζ62ζ600−2ζ22ζ200000000000000000000
χ4922-2-2−2i2i−2i2i00−2i2i2-200-2-22222−2−2−i2−i2i2i22i2i−2i−2i0000002−2−i2i2−2−222i2i2−i2−i21+i−1−i−1−i1+i−1+i1−i1−i−1+i−2ζ22ζ200−2ζ62ζ60000000000000000000000
χ5022-2-2−2i2i−2i2i00−2i2i2-200-2-22222−2−2−i2−i2i2i22i2i−2i−2i0000002−2−i2i2−2−222i2i2−i2−i2−1−i1+i1+i−1−i1−i−1+i−1+i1−i2ζ2−2ζ2002ζ6−2ζ60000000000000000000000
χ5122-2-2−2i2i−2i2i00−2i2i2-200-2-222−2−222i2i2−i2−i22i2i−2i−2i000000−22i2−i222−2−2−i2−i2i2i21+i−1−i−1−i1+i−1+i1−i1−i−1+i2ζ2−2ζ2002ζ6−2ζ60000000000000000000000
χ5222-2-2−2i2i−2i2i00−2i2i2-200-2-222−2−222i2i2−i2−i22i2i−2i−2i000000−22i2−i222−2−2−i2−i2i2i2−1−i1+i1+i−1−i1−i−1+i−1+i1−i−2ζ22ζ200−2ζ62ζ60000000000000000000000
χ532-2-2222-2-22-200002-22−22−22-22-22-22-22−22−2002−22−200002−22−22−22−20000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000
χ542-2-2222-2-22-200002-22−22−22-22-22-22-22−22−2002−22−200002−22−22−22−20000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000
χ552-2-2222-2-22-200002-22−22−2-22-22-22-222−22−2002−22−20000−22−22−22−220000000000000000ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ50000
χ562-2-2222-2-22-200002-22−22−2-22-22-22-222−22−2002−22−20000−22−22−22−220000000000000000−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ50000
χ572-2-2222-2-22-200002-2−22−222-22-22-22-2−22−2200−22−220000−22−22−22−220000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000
χ582-2-2222-2-22-200002-2−22−222-22-22-22-2−22−2200−22−220000−22−22−22−220000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000
χ592-2-2222-2-22-200002-2−22−22-22-22-22-22−22−2200−22−2200002−22−22−22−20000000000000000ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ70000
χ602-2-2222-2-22-200002-2−22−22-22-22-22-22−22−2200−22−2200002−22−22−22−20000000000000000−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ70000
χ612-2-22-2-222-2200002-22−22−22-22-2-22-22−22−22002−2−2200002−22−2−22−220000000000000000ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ622-2-22-2-222-2200002-22−22−22-22-2-22-22−22−22002−2−2200002−22−2−22−220000000000000000−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ632-2-22-2-222-2200002-22−22−2-22-222-22-2−22−22002−2−220000−22−222−22−20000000000000000ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ642-2-22-2-222-2200002-22−22−2-22-222-22-2−22−22002−2−220000−22−222−22−20000000000000000−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ652-2-22-2-222-2200002-2−22−222-22-2-22-222−22−200−222−20000−22−222−22−20000000000000000ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ662-2-22-2-222-2200002-2−22−222-22-2-22-222−22−200−222−20000−22−222−22−20000000000000000−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ672-2-22-2-222-2200002-2−22−22-22-222-22-22−22−200−222−200002−22−2−22−220000000000000000ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ682-2-22-2-222-2200002-2−22−22-22-222-22-22−22−200−222−200002−22−2−22−220000000000000000−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ6944444444-4-4-4-4-4-4-4-40000000000000000440000000000000000000000000000000000000000000000000000
χ704444-4-4-4-44444-4-4-4-40000000000000000-440000000000000000000000000000000000000000000000000000
χ7144-4-44i−4i4i−4i00−4i4i-440000002222−22−222i22i2−2i2−2i20000000000−2222−2i22i200000000000000000000000000000000000000000000
χ7244-4-44i−4i4i−4i00−4i4i-44000000−22−222222−2i2−2i22i22i2000000000022−222i2−2i200000000000000000000000000000000000000000000
χ7344-4-4−4i4i−4i4i004i−4i-440000002222−22−22−2i2−2i22i22i20000000000−22222i2−2i200000000000000000000000000000000000000000000
χ7444-4-4−4i4i−4i4i004i−4i-44000000−22−2222222i22i2−2i2−2i2000000000022−22−2i22i200000000000000000000000000000000000000000000
χ754-44-44i−4i−4i4i0000000022−22−222222−22−22222i2−2i2−2i22i22i2−2i2−2i22i200000000002-2-222i−2i−2i2i000000000000000000000000000000000000
χ764-44-44i−4i−4i4i0000000022−22−2222−222222−22−2i22i22i2−2i22i2−2i2−2i22i20000000000-222-2−2i2i2i−2i000000000000000000000000000000000000
χ774-44-44i−4i−4i4i00000000−222222−2222−22−22222i2−2i2−2i22i2−2i22i22i2−2i20000000000-222-2−2i2i2i−2i000000000000000000000000000000000000
χ784-44-44i−4i−4i4i00000000−222222−22−222222−22−2i22i22i2−2i2−2i22i22i2−2i200000000002-2-222i−2i−2i2i000000000000000000000000000000000000
χ794-44-4−4i4i4i−4i0000000022−22−222222−22−2222−2i22i22i2−2i2−2i22i22i2−2i200000000002-2-22−2i2i2i−2i000000000000000000000000000000000000
χ804-44-4−4i4i4i−4i0000000022−22−2222−222222−222i2−2i2−2i22i2−2i22i22i2−2i20000000000-222-22i−2i−2i2i000000000000000000000000000000000000
χ814-44-4−4i4i4i−4i00000000−222222−2222−22−2222−2i22i22i2−2i22i2−2i2−2i22i20000000000-222-22i−2i−2i2i000000000000000000000000000000000000
χ824-44-4−4i4i4i−4i00000000−222222−22−222222−222i2−2i2−2i22i22i2−2i2−2i22i200000000002-2-22−2i2i2i−2i000000000000000000000000000000000000
χ834-4-4444-4-4-440000-4422−2222−220000000022−2222−2200−2222−2222000000000000000000000000000000000000000000000000
χ844-4-4444-4-4-440000-44−2222−222200000000−2222−22220022−2222−22000000000000000000000000000000000000000000000000
χ854-4-44-4-4444-40000-4422−2222−2200000000−2222−222200−222222−22000000000000000000000000000000000000000000000000
χ864-4-44-4-4444-40000-44−2222−22220000000022−2222−220022−22−2222000000000000000000000000000000000000000000000000

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