Finite Group Databasebeta

← Group #13041475

Character table — Group #13041475

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89
size1111222244444444444555588888881010101010101010101010101010101010101010161616161616161616202020202020202020202020202020202020203232404040404040404040
order12224444444588881010102222444202020204444444444448888888820202020204040404044444444444888888882020444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1
χ31111111111111111111-1-1-1-11111111-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i111111111-1-1-1iiii−i−i−i−i-1-1-1-1ii−i−i11-1-1-1i−iii−i−i
χ41111111111111111111-1-1-1-11111111-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii111111111-1-1-1−i−i−i−iiiii-1-1-1-1−i−iii11-1-1-1−ii−i−iii
χ5111111111111-1-1-1-111111111-1-11111111111111111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111
χ6111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-1111-1-111-1-111-1-1-1-11111-1-11-1-111-1-1-1-1
χ7111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1iiii−i−i−i−i-1-1−i−i−i−iiiii11111-1-1-1-1-1-1-1ii−i−i−i−iii1111−i−iii-1-1-111−iiii−i−i
χ8111111111111-1-1-1-1111-1-1-1-11-1-11111-1-1−i−i−i−iiiii-1-1iiii−i−i−i−i11111-1-1-1-1-1-1-1−i−iiiii−i−i1111ii−i−i-1-1-111i−i−i−iii
χ9111111111-1-1111111111111-1-1-11111111111111111111111111-1-1-1-111111-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1
χ10111111111-1-1111111111111-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1111111
χ11111111111-1-111111111-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i-1-1iiii−i−i−i−i1-1-1-1-11111-111ii−i−i−i−iii-1-1-1-1ii−i−i-1-1111−ii−i−iii
χ12111111111-1-111111111-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii-1-1−i−i−i−iiiii1-1-1-1-11111-111−i−iiiii−i−i-1-1-1-1−i−iii-1-1111i−iii−i−i
χ13111111111-1-11-1-1-1-11111111-1111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-111-11111-1-1-1-1
χ14111111111-1-11-1-1-1-11111111-111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-11111
χ15111111111-1-11-1-1-1-1111-1-1-1-1-1111111-1-1iiii−i−i−i−i-1-1−i−i−i−iiiii1-1-1-1-1-1-1-1-1-111iiii−i−i−i−i1111−i−iii111-1-1i−i−i−iii
χ16111111111-1-11-1-1-1-1111-1-1-1-1-1111111-1-1−i−i−i−iiiii-1-1iiii−i−i−i−i1-1-1-1-1-1-1-1-1-111−i−i−i−iiiii1111ii−i−i111-1-1−iiii−i−i
χ171111-1-111-111111-1-11111111-11-1-1-111-1-111-1-111-1-11111111111-1-1-11111-1-1-1111-1111-11111-1-1-1-1-1-11-1-11-1-1-11-11-1
χ181111-1-111-111111-1-11111111-11-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-11-1-1-11-1-111-1-111111-1-11-111-11-11
χ191111-1-111-111111-1-1111-1-1-1-1-11-1-1-11111ii−i−i−i−iii-1-1iiii−i−i−i−i-1-1-11111-1-11-1-1i−iii−ii−i−i-1-111−i−iii1-11-11−iii−i−ii
χ201111-1-111-111111-1-1111-1-1-1-1-11-1-1-11111−i−iiiii−i−i-1-1−i−i−i−iiiii-1-1-11111-1-11-1-1−ii−i−ii−iii-1-111ii−i−i1-11-11i−i−iii−i
χ211111-1-111-1111-1-1111111111-1-11-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-111-1111-1-1-11-1-1-1-1-1111111-11-1-11111-11-1
χ221111-1-111-1111-1-1111111111-1-11-1-111-1-1-1-111-1-1111111111111-1-1-111-1-111-111-1111-1111-1-111-1-1-1-1-11-1-11-1-1-11-11
χ231111-1-111-1111-1-111111-1-1-1-1-1-11-1-11111ii−i−i−i−iii-1-1−i−i−i−iiiii-1-1-111-1-1111-1-1i−i−i−i−iiii11-1-1ii−i−i-1111-1i−ii−i−ii
χ241111-1-111-1111-1-111111-1-1-1-1-1-11-1-11111−i−iiiii−i−i-1-1iiii−i−i−i−i-1-1-111-1-1111-1-1−iiiii−i−i−i11-1-1−i−iii-1111-1−ii−iii−i
χ251111-1-111-1-1-1111-1-111111111-11-1-111-1-111-1-111-1-11111111111-111-1-111-1-1-1-1-11-1-1-11-1-1-111-1-1-1-1-1-1-111-1111-11-11
χ261111-1-111-1-1-1111-1-111111111-11-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1111-111111-1-11111-111-11-1-11-11-1
χ271111-1-111-1-1-1111-1-1111-1-1-1-11-11-1-11111ii−i−i−i−iii-1-1iiii−i−i−i−i-111-1-111-1-1111i−i−i−i−iiii-1-111−i−iii-11-11-1i−i−iii−i
χ281111-1-111-1-1-1111-1-1111-1-1-1-11-11-1-11111−i−iiiii−i−i-1-1−i−i−i−iiiii-111-1-111-1-1111−iiiii−i−i−i-1-111ii−i−i-11-11-1−iii−i−ii
χ291111-1-111-1-1-11-1-111111111111-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-11-1111-111-1-11111111-111-1-1-1-11-11
χ301111-1-111-1-1-11-1-111111111111-1-1-111-1-1-1-111-1-1111111111111-111-1-1-1-111-1-1-1-11-1-1-11-1-1-1-111-1-1-1-11-111-1111-11-1
χ311111-1-111-1-1-11-1-111111-1-1-1-111-1-1-11111ii−i−i−i−iii-1-1−i−i−i−iiiii-111-1-1-1-111111i−iii−ii−i−i11-1-1ii−i−i1-1-1-11−ii−iii−i
χ321111-1-111-1-1-11-1-111111-1-1-1-111-1-1-11111−i−iiiii−i−i-1-1iiii−i−i−i−i-111-1-1-1-111111−ii−i−ii−iii11-1-1−i−iii1-1-1-11i−ii−i−ii
χ33222222-2-2-20020000222222200022-2-22222222222-2-200000000-200000000-200-2-200-2-2000000000000000000000
χ34222222-2-2-20020000222222200022-2-222-2-2-2-2-2-2-2-2-2-200000000-200000000-200220022000000000000000000000
χ35222222-2-2-20020000222-2-2-2-200022-2-2-2-22i2i2i2i−2i−2i−2i−2i2200000000-200000000200−2i−2i002i2i000000000000000000000
χ36222222-2-2-20020000222-2-2-2-200022-2-2-2-2−2i−2i−2i−2i2i2i2i2i2200000000-2000000002002i2i00−2i−2i000000000000000000000
χ372222-2-2-2-2200200002222222000-2-2-2-2-2-222-2-222-2-2-2-200000000200000000200-2200-22000000000000000000000
χ382222-2-2-2-2200200002222222000-2-2-2-2-2-2-2-222-2-222-2-2000000002000000002002-2002-2000000000000000000000
χ392222-2-2-2-220020000222-2-2-2-2000-2-2-2-2222i2i−2i−2i−2i−2i2i2i2200000000200000000-200−2i2i002i−2i000000000000000000000
χ402222-2-2-2-220020000222-2-2-2-2000-2-2-2-222−2i−2i2i2i2i2i−2i−2i2200000000200000000-2002i−2i00−2i2i000000000000000000000
χ4122-2-22-20000022−22−22-2-222-2-20002-2002-22-22-22-22-20022−2−222−2−2000002−22−2000000000002−22−22−22−200000000000
χ4222-2-22-20000022−22−22-2-222-2-20002-2002-2-22-22-22-2200−2−222−2−222000002−22−2000000000002−22−2−22−2200000000000
χ4322-2-22-20000022−22−22-2-2-2-2220002-200-222i−2i2i−2i−2i2i−2i2i00i2i2−i2−i2−i2−i2i2i2000002−22−200000000000−22−22i2−i2−i2i200000000000
χ4422-2-22-20000022−22−22-2-2-2-2220002-200-22−2i2i−2i2i2i−2i2i−2i00−i2−i2i2i2i2i2−i2−i2000002−22−200000000000−22−22−i2i2i2−i200000000000
χ4522-2-22-2000002−22−222-2-222-2-20002-2002-22-22-22-22-200−2−222−2−22200000−22−2200000000000−22−22−22−2200000000000
χ4622-2-22-2000002−22−222-2-222-2-20002-2002-2-22-22-22-220022−2−222−2−200000−22−2200000000000−22−222−22−200000000000
χ4722-2-22-2000002−22−222-2-2-2-2220002-200-222i−2i2i−2i−2i2i−2i2i00−i2−i2i2i2i2i2−i2−i200000−22−22000000000002−22−2−i2i2i2−i200000000000
χ4822-2-22-2000002−22−222-2-2-2-2220002-200-22−2i2i−2i2i2i−2i2i−2i00i2i2−i2−i2−i2−i2i2i200000−22−22000000000002−22−2i2−i2−i2i200000000000
χ4922-2-2-220000022−2−222-2-222-2-2000-2200-222-2-222-2-220022−2−222−2−2000002−2−22000000000002−2−22−22−2200000000000
χ5022-2-2-220000022−2−222-2-222-2-2000-2200-22-222-2-222-200−2−222−2−222000002−2−22000000000002−2−222−22−200000000000
χ5122-2-2-220000022−2−222-2-2-2-222000-22002-22i−2i−2i2i−2i2i2i−2i00i2i2−i2−i2−i2−i2i2i2000002−2−2200000000000−222−2−i2i2i2−i200000000000
χ5222-2-2-220000022−2−222-2-2-2-222000-22002-2−2i2i2i−2i2i−2i−2i2i00−i2−i2i2i2i2i2−i2−i2000002−2−2200000000000−222−2i2−i2−i2i200000000000
χ5322-2-2-22000002−222−22-2-222-2-2000-2200-222-2-222-2-2200−2−222−2−22200000−222−200000000000−222−22−22−200000000000
χ5422-2-2-22000002−222−22-2-222-2-2000-2200-22-222-2-222-20022−2−222−2−200000−222−200000000000−222−2−22−2200000000000
χ5522-2-2-22000002−222−22-2-2-2-222000-22002-22i−2i−2i2i−2i2i2i−2i00−i2−i2i2i2i2i2−i2−i200000−222−2000000000002−2−22i2−i2−i2i200000000000
χ5622-2-2-22000002−222−22-2-2-2-222000-22002-2−2i2i2i−2i2i−2i−2i2i00i2i2−i2−i2−i2−i2i2i200000−222−2000000000002−2−22−i2i2i2−i200000000000
χ572-2-2200-2202-220000-2-222-22-200000-2200000000002-22i−2i2i−2i2i−2i2i−2i0002-2000002-2002i−2i002i−2i0000000000000000000
χ582-2-2200-2202-220000-2-222-22-200000-2200000000002-2−2i2i−2i2i−2i2i−2i2i0002-2000002-200−2i2i00−2i2i0000000000000000000
χ592-2-2200-2202-220000-2-22-22-2200000-220000000000-222-22-2-22-220002-200000-22002-200-220000000000000000000
χ602-2-2200-2202-220000-2-22-22-2200000-220000000000-22-22-222-22-20002-200000-2200-22002-20000000000000000000
χ612-2-2200-220-2220000-2-222-22-200000-2200000000002-22i−2i2i−2i2i−2i2i−2i000-2200000-2200−2i2i00−2i2i0000000000000000000
χ622-2-2200-220-2220000-2-222-22-200000-2200000000002-2−2i2i−2i2i−2i2i−2i2i000-2200000-22002i−2i002i−2i0000000000000000000
χ632-2-2200-220-2220000-2-22-22-2200000-220000000000-222-22-2-22-22000-22000002-200-22002-20000000000000000000
χ642-2-2200-220-2220000-2-22-22-2200000-220000000000-22-22-222-22-2000-22000002-2002-200-220000000000000000000
χ6544444444444-14444-1-1-10000444-1-1-1-100000000000000000000-1-1-1-1-1-1-1-1-10000000000000000000-1-1000000000
χ6644444444444-1-4-4-4-4-1-1-100004-4-4-1-1-1-100000000000000000000-1-1-1-1-11111000000000000000000011000000000
χ67444444444-4-4-14444-1-1-10000-4-4-4-1-1-1-100000000000000000000-11111-1-1-1-1000000000000000000011000000000
χ68444444444-4-4-1-4-4-4-4-1-1-10000-444-1-1-1-100000000000000000000-1111111110000000000000000000-1-1000000000
χ694444-4-444-444-144-4-4-1-1-10000-44-411-1-100000000000000000000111-1-1-1-1110000000000000000000-11000000000
χ704444-4-444-444-1-4-444-1-1-10000-4-4411-1-100000000000000000000111-1-111-1-100000000000000000001-1000000000
χ714444-4-444-4-4-4-144-4-4-1-1-100004-4411-1-1000000000000000000001-1-111-1-11100000000000000000001-1000000000
χ724444-4-444-4-4-4-1-4-444-1-1-1000044-411-1-1000000000000000000001-1-11111-1-10000000000000000000-11000000000
χ734-44-4000000040000-44-44-4-4400000000000000000002i2−2i2−2i22i22i2−2i2−2i22i2000000000000000000000000000000000000000
χ744-44-4000000040000-44-44-4-440000000000000000000−2i22i22i2−2i2−2i22i22i2−2i2000000000000000000000000000000000000000
χ754-44-4000000040000-44-4-444-4000000000000000000022−22−2222−222222−22000000000000000000000000000000000000000
χ764-44-4000000040000-44-4-444-40000000000000000000−222222−2222−22−2222000000000000000000000000000000000000000
χ774-4-44004-400040000-4-444-44-4000004-40000000000-4400000000000000000000000000000000000000000000000
χ784-4-44004-400040000-4-44-44-44000004-400000000004-400000000000000000000000000000000000000000000000
χ79888888-8-8-800-20000-2-2-20000000-2-22200000000000000000000200000000000000000000000000000000000000
χ808888-8-8-8-8800-20000-2-2-20000000222200000000000000000000-200000000000000000000000000000000000000
χ8188-8-88-800000-242−4242−42-2220000000-22000000000000000000000000000−22−22000000000000000000000000000000
χ8288-8-88-800000-2−4242−4242-2220000000-220000000000000000000000000002−22−2000000000000000000000000000000
χ8388-8-8-8800000-242−42−4242-22200000002-2000000000000000000000000000−222−2000000000000000000000000000000
χ8488-8-8-8800000-2−424242−42-22200000002-20000000000000000000000000002−2−22000000000000000000000000000000
χ858-8-88008-8000-2000022-2000000000-220000000000000000000002i5−2i5000000000000000000000000000000000000
χ868-8-88008-8000-2000022-2000000000-22000000000000000000000−2i52i5000000000000000000000000000000000000
χ878-8-8800-8808-8-2000022-20000000002-200000000000000000000000-220000000000000000000000000000000000
χ888-8-8800-880-88-2000022-20000000002-2000000000000000000000002-20000000000000000000000000000000000
χ8916-1616-160000000-400004-440000000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).