Finite Group Databasebeta

← Group #13036849

Character table — Group #13036849

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size111122222222222222444455555555555588888888888888888810101010101010101010101010101010101010101010101010101010101010101010101010101010101032323232404040404040404040404040
order12224444448888888851010104444888888884444202020202020404040404040404022444444444444444444448888888888888888888820202020222288888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111-1-1-1-1iiii−i−i−i−i111111111111111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i1111-1-1-1-1iiii−i−i−i−i
χ61111111111111111111111-1-1-1-1iiii−i−i−i−i-1-1-1-111111111111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-1-1-1-1-1iiii−i−i−i−iii−i−i-1-1-1-11111−i−i−i−iiiii
χ71111111111111111111111-1-1-1-1−i−i−i−iiiii111111111111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii1111-1-1-1-1−i−i−i−iiiii
χ81111111111111111111111-1-1-1-1−i−i−i−iiiii-1-1-1-111111111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−iii-1-1-1-11111iiii−i−i−i−i
χ91111111111-1-1-1-1-1-1-1-1111111111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-1-111-1-111-1-1
χ101111111111-1-1-1-1-1-1-1-11111111111111111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111-1-111-1-111
χ111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111
χ121111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-1
χ131111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111iiii−i−i−i−iii−i−i11-1-1-1-111ii−i−i−i−iii
χ141111111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11111111iiii−i−i−i−iii−i−i-1-11111-1-1−i−iiiii−i−i
χ151111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii11-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111−i−i−i−iiiii−i−iii11-1-1-1-111−i−iiiii−i−i
χ161111111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11111111−i−i−i−iiiii−i−iii-1-11111-1-1ii−i−i−i−iii
χ171111-1-1-1-1111111-1-1-1-111111111111111111-11-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-11-11-11-11-11-11-11-1
χ181111-1-1-1-1111111-1-1-1-11111111111111111-11-11-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-11-11-11-11-11-11
χ191111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-11-11-11-11-1-11-11-11-11
χ201111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-11-11-11-111-11-11-11-1
χ211111-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−i1-11-1-1-1-1-1111111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiiiii−i−i1-11-1-11-11i−ii−i−ii−ii
χ221111-1-1-1-1111111-1-1-1-11111-1-1-1-1iiii−i−i−i−i-11-11-1-1-1-1111111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111−i−i−i−iiiiiii−i−i-11-111-11-1−ii−iii−ii−i
χ231111-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii1-11-1-1-1-1-1111111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i−i−iii1-11-1-11-11−ii−iii−ii−i
χ241111-1-1-1-1111111-1-1-1-11111-1-1-1-1−i−i−i−iiiii-11-11-1-1-1-1111111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-11111iiii−i−i−i−i−i−iii-11-111-11-1i−ii−i−ii−ii
χ251111-1-1-1-111-1-1-1-1111111111111111111111-1-11-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-111-1-111-1-111-1-11
χ261111-1-1-1-111-1-1-1-111111111111111111111-111-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-111-1-111-1-111-1
χ271111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-11-1-11-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11-1-111-1-11-111-1-111-1
χ281111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-111-1-111-11-1-111-1-11
χ291111-1-1-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i1-1-11-1-1-1-111-1-1-1-11111-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiiii−i−i1-1-11-111-1i−i−ii−iii−i
χ301111-1-1-1-111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i-111-1-1-1-1-111-1-1-1-11111-1-11111−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−i−i−i−iiiiiii−i−i-111-11-1-11−iii−ii−i−ii
χ311111-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii1-1-11-1-1-1-111-1-1-1-11111-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−i−iii1-1-11-111-1−iii−ii−i−ii
χ321111-1-1-1-111-1-1-1-111111111-1-1-1-1−i−i−i−iiiii-111-1-1-1-1-111-1-1-1-11111-1-11111iiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1iiii−i−i−i−i−i−iii-111-11-1-11i−i−ii−iii−i
χ33222222-2-2-2-2000000002222222222222222000022-2-2-2-200000000-2-222-2-200000000000000000000000022-2-222-2-2-2-2-2-20000000000000000
χ34222222-2-2-2-20000000022222222-2-2-2-2-2-2-2-2000022-2-2-2-200000000-2-222-2-2000000000000000000000000-2-222-2-22222220000000000000000
χ35222222-2-2-2-2000000002222-2-2-2-22i2i2i2i−2i−2i−2i−2i000022-2-2-2-20000000022-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000
χ36222222-2-2-2-2000000002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i000022-2-2-2-20000000022-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000
χ372222-2-222-2-20000000022222222222222220000-2-222-2-200000000-2-2-2-222000000000000000000000000-2-222-2-222-2-2-2-20000000000000000
χ382222-2-222-2-20000000022222222-2-2-2-2-2-2-2-20000-2-222-2-200000000-2-2-2-22200000000000000000000000022-2-222-2-222220000000000000000
χ392222-2-222-2-2000000002222-2-2-2-22i2i2i2i−2i−2i−2i−2i0000-2-222-2-2000000002222-2-2000000000000000000000000−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-222-2-2000000002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i0000-2-222-2-2000000002222-2-20000000000000000000000002i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000
χ4122-2-2002-20022−2−222−2−222-2-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000002-20022−2−222−2−200002i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+ii2i2−i2−i2i2i2−i2−i2002ζ−2ζ002ζ3−2ζ300000000000000000000
χ4222-2-2002-20022−2−222−2−222-2-22i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000002-20022−2−222−2−200002i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−ii2i2−i2−i2i2i2−i2−i200−2ζ2ζ00−2ζ32ζ300000000000000000000
χ4322-2-2002-20022−2−222−2−222-2-2−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000002-20022−2−222−2−20000−2i2i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−i2−i2i2i2−i2−i2i2i2002ζ3−2ζ3002ζ−2ζ00000000000000000000
χ4422-2-2002-20022−2−222−2−222-2-2−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000002-20022−2−222−2−20000−2i2i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i−i2−i2i2i2−i2−i2i2i200−2ζ32ζ300−2ζ2ζ00000000000000000000
χ4522-2-2002-200−2−222−2−22222-2-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000002-200−2−222−2−22200002i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−i2−i2i2i2−i2−i2i2i2002ζ−2ζ002ζ3−2ζ300000000000000000000
χ4622-2-2002-200−2−222−2−22222-2-22i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000002-200−2−222−2−22200002i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i−i2−i2i2i2−i2−i2i2i200−2ζ2ζ00−2ζ32ζ300000000000000000000
χ4722-2-2002-200−2−222−2−22222-2-2−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000002-200−2−222−2−2220000−2i2i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−ii2i2−i2−i2i2i2−i2−i2002ζ3−2ζ3002ζ−2ζ00000000000000000000
χ4822-2-2002-200−2−222−2−22222-2-2−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000002-200−2−222−2−2220000−2i2i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+ii2i2−i2−i2i2i2−i2−i200−2ζ32ζ300−2ζ2ζ00000000000000000000
χ4922-2-200-220022−2−2−2−22222-2-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000-220022−2−2−2−2220000−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−ii2i2−i2−i2−i2−i2i2i200−2ζ2ζ00−2ζ32ζ300000000000000000000
χ5022-2-200-220022−2−2−2−22222-2-22i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000-220022−2−2−2−2220000−2i2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+ii2i2−i2−i2−i2−i2i2i2002ζ−2ζ002ζ3−2ζ300000000000000000000
χ5122-2-200-220022−2−2−2−22222-2-2−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000-220022−2−2−2−22200002i−2i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−i2−i2i2i2i2i2−i2−i200−2ζ32ζ300−2ζ2ζ00000000000000000000
χ5222-2-200-220022−2−2−2−22222-2-2−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000-220022−2−2−2−22200002i−2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−i2−i2i2i2i2i2−i2−i2002ζ3−2ζ3002ζ−2ζ00000000000000000000
χ5322-2-200-2200−2−22222−2−222-2-22i−2i2i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000-2200−2−22222−2−20000−2i2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−i2−i2i2i2i2i2−i2−i200−2ζ2ζ00−2ζ32ζ300000000000000000000
χ5422-2-200-2200−2−22222−2−222-2-22i−2i2i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000-2200−2−22222−2−20000−2i2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−i2−i2i2i2i2i2−i2−i2002ζ−2ζ002ζ3−2ζ300000000000000000000
χ5522-2-200-2200−2−22222−2−222-2-2−2i2i−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000-2200−2−22222−2−200002i−2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+ii2i2−i2−i2−i2−i2i2i200−2ζ32ζ300−2ζ2ζ00000000000000000000
χ5622-2-200-2200−2−22222−2−222-2-2−2i2i−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000-2200−2−22222−2−200002i−2i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−ii2i2−i2−i2−i2−i2i2i2002ζ3−2ζ3002ζ−2ζ00000000000000000000
χ572-22-22-200002−22−22−22−22-22-22i−2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00002-200002−22−22−22−2002i−2i001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−ii2−i2i2−i2i2−i2i2−i22ζ3−2ζ3002ζ−2ζ0000000000000000000000
χ582-22-22-200002−22−22−22−22-22-22i−2i−2i2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00002-200002−22−22−22−2002i−2i00−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+ii2−i2i2−i2i2−i2i2−i2−2ζ32ζ300−2ζ2ζ0000000000000000000000
χ592-22-22-200002−22−22−22−22-22-2−2i2i2i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300002-200002−22−22−22−200−2i2i00−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i−i2i2−i2i2−i2i2−i2i22ζ−2ζ002ζ3−2ζ30000000000000000000000
χ602-22-22-200002−22−22−22−22-22-2−2i2i2i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300002-200002−22−22−22−200−2i2i001+i−1−i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i−i2i2−i2i2−i2i2−i2i2−2ζ2ζ00−2ζ32ζ30000000000000000000000
χ612-22-22-20000−22−22−22−222-22-22i−2i−2i2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00002-20000−22−22−22−22002i−2i00−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−i2i2−i2i2−i2i2−i2i22ζ3−2ζ3002ζ−2ζ0000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.