Finite Group Databasebeta

← Group #10815957

Character table — Group #10815957

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222224444444444444444444444666666666666666688888888888888888888888812121212121212121212121216161616242424242424
order12224444223446668888121212124444668888888888121224242424224444444444888822446688121212121212242424242424242424242224448888886122424448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-1111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-111-111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111-1-1-1-111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111111-11-111-1-111-1-1-1-1111111-1-1-1-11-1-11-1-111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111-1-1-1-111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-11-11-111-1-111-1-1-1-1111111-1-1-1-1-111-111-1-11111-1-1-1-1-1-1-1-111
χ7111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-11-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
χ8111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-11-11-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111111111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-11-11-1-1-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1
χ101111111111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111
χ111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-11111-1-111
χ121111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11-11111111111-1-1-1-1-1-1-1-1-1-1-111-111111111-1-111-1-111-1-1
χ131111111111111111-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-11111-1-111-1-11111
χ141111111111111111-1-1-1-11111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-111-11111-1-1-1-1-1-11111-1-1-1-1
χ151111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-111-1-1-1-1
χ161111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1-1-11111
χ171111-1-1-1-1-1-1111111ii−i−i-1-1-1-1ii−i−i-1-1i−iii−i−i11-1-111ii−i−i11-1-1iiii−i−i−i−iii−i−i11-1-111i−i-1-1ii−i−ii−iii−i−i11-1-1-1111-1-1i−i11-1-11-1i−i1-1i−ii−i
χ181111-1-1-1-1-1-1111111ii−i−i-1-1-1-1ii−i−i-1-1i−iii−i−i11-1-111ii−i−i-1-111−i−i−i−iiiii−i−iii11-1-111i−i-1-1ii−i−ii−iii−i−i11-1-11-1-1-111−ii-1-1111-1i−i-11−ii−ii
χ191111-1-1-1-1-1-1111111ii−i−i-1-1-1-1ii−i−i-1-1i−i−i−iii11-1-111ii−i−i11-1-1iiii−i−i−i−iii−i−i-1-111-1-1−ii11ii−i−ii−i−i−iii11-1-1-1-1-1111i−i11-1-1-11−ii-11−ii−ii
χ201111-1-1-1-1-1-1111111ii−i−i-1-1-1-1ii−i−i-1-1i−i−i−iii11-1-111ii−i−i-1-111−i−i−i−iiiii−i−iii-1-111-1-1−ii11ii−i−ii−i−i−iii11-1-1111-1-1-1−ii-1-111-11−ii1-1i−ii−i
χ211111-1-1-1-1-1-1111111ii−i−i-1-1-1-1−i−iii-1-1i−iii−i−i-1-11111ii−i−i11-1-1−i−i−i−iiiiiii−i−i1-1-1111−ii-1-1−i−iiii−iii−i−i-1-111-1-1-1111i−i-1-111-11−ii1-1i−i−ii
χ221111-1-1-1-1-1-1111111ii−i−i-1-1-1-1−i−iii-1-1i−iii−i−i-1-11111ii−i−i-1-111iiii−i−i−i−i−i−iii1-1-1111−ii-1-1−i−iiii−iii−i−i-1-111111-1-1-1−ii11-1-1-11−ii-11−iii−i
χ231111-1-1-1-1-1-1111111ii−i−i-1-1-1-1−i−iii-1-1i−i−i−iii-1-11111ii−i−i11-1-1−i−i−i−iiiiiii−i−i-111-1-1-1i−i11−i−iiii−i−i−iii-1-111-1111-1-1i−i-1-1111-1i−i-11−iii−i
χ241111-1-1-1-1-1-1111111ii−i−i-1-1-1-1−i−iii-1-1i−i−i−iii-1-11111ii−i−i-1-111iiii−i−i−i−i−i−iii-111-1-1-1i−i11−i−iiii−i−i−iii-1-1111-1-1-111−ii11-1-11-1i−i1-1i−i−ii
χ251111-1-1-1-1-1-1111111−i−iii-1-1-1-1ii−i−i-1-1−iiii−i−i-1-11111−i−iii11-1-1iiii−i−i−i−i−i−iii-111-1-1-1−ii11ii−i−i−iiii−i−i-1-111-1111-1-1−ii-1-1111-1−ii-11i−i−ii
χ261111-1-1-1-1-1-1111111−i−iii-1-1-1-1ii−i−i-1-1−iiii−i−i-1-11111−i−iii-1-111−i−i−i−iiiiiii−i−i-111-1-1-1−ii11ii−i−i−iiii−i−i-1-1111-1-1-111i−i11-1-11-1−ii1-1−iii−i
χ271111-1-1-1-1-1-1111111−i−iii-1-1-1-1ii−i−i-1-1−ii−i−iii-1-11111−i−iii11-1-1iiii−i−i−i−i−i−iii1-1-1111i−i-1-1ii−i−i−ii−i−iii-1-111-1-1-1111−ii-1-111-11i−i1-1−iii−i
χ281111-1-1-1-1-1-1111111−i−iii-1-1-1-1ii−i−i-1-1−ii−i−iii-1-11111−i−iii-1-111−i−i−i−iiiiiii−i−i1-1-1111i−i-1-1ii−i−i−ii−i−iii-1-111111-1-1-1i−i11-1-1-11i−i-11i−i−ii
χ291111-1-1-1-1-1-1111111−i−iii-1-1-1-1−i−iii-1-1−iiii−i−i11-1-111−i−iii11-1-1−i−i−i−iiiii−i−iii-1-111-1-1i−i11−i−iii−iiii−i−i11-1-1-1-1-1111−ii11-1-1-11i−i-11i−ii−i
χ301111-1-1-1-1-1-1111111−i−iii-1-1-1-1−i−iii-1-1−iiii−i−i11-1-111−i−iii-1-111iiii−i−i−i−iii−i−i-1-111-1-1i−i11−i−iii−iiii−i−i11-1-1111-1-1-1i−i-1-111-11i−i1-1−ii−ii
χ311111-1-1-1-1-1-1111111−i−iii-1-1-1-1−i−iii-1-1−ii−i−iii11-1-111−i−iii11-1-1−i−i−i−iiiii−i−iii11-1-111−ii-1-1−i−iii−ii−i−iii11-1-1-1111-1-1−ii11-1-11-1−ii1-1−ii−ii
χ321111-1-1-1-1-1-1111111−i−iii-1-1-1-1−i−iii-1-1−ii−i−iii11-1-111−i−iii-1-111iiii−i−i−i−iii−i−i11-1-111−ii-1-1−i−iii−ii−i−iii11-1-11-1-1-111i−i-1-1111-1−ii-11i−ii−i
χ332222222222-122-1-1-12222-1-1-1-12222-1-12222222222-1-1-1-1-1-100000000000000002222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000-1-1-1-1000000
χ342222222222-122-1-1-12222-1-1-1-12222-1-122-2-2-2-22222-1-1-1-1-1-10000000000000000-2-2-2-211-2-211-1-1-1-1-1-11111-1-1-1-10000000000001111000000
χ352222222222-122-1-1-12222-1-1-1-1-2-2-2-2-1-1222222-2-2-2-2-1-1-1-1-1-100000000000000002-22-2-1-1-2-2-1-11111-1-1-1-1-1-111110000000000001111000000
χ362222222222-122-1-1-12222-1-1-1-1-2-2-2-2-1-122-2-2-2-2-2-2-2-2-1-1-1-1-1-10000000000000000-22-221122111111-1-111111111000000000000-1-1-1-1000000
χ372222222222-122-1-1-1-2-2-2-2-1-1-1-12222-1-1-2-22222-2-2-2-2-1-111110000000000000000-22-2211-2-211-1-1-1-111-1-1-1-11111000000000000-1-111000000
χ382222222222-122-1-1-1-2-2-2-2-1-1-1-12222-1-1-2-2-2-2-2-2-2-2-2-2-1-1111100000000000000002-22-2-1-122-1-1-1-1-1-1111111111100000000000011-1-1000000
χ392222222222-122-1-1-1-2-2-2-2-1-1-1-1-2-2-2-2-1-1-2-222222222-1-111110000000000000000-2-2-2-2112211111111-1-1-1-1-1-1-1-100000000000011-1-1000000
χ402222222222-122-1-1-1-2-2-2-2-1-1-1-1-2-2-2-2-1-1-2-2-2-2-2-22222-1-1111100000000000000002222-1-1-2-2-1-11111111111-1-1-1-1000000000000-1-111000000
χ4122222222-2-22-2-2222222222220000-2-2-2-200000000-2-22222222200000000222200000000000000-2-200000000-200-200-2-200000000000000
χ4222222222-2-22-2-2222222222220000-2-2-2-200000000-2-22222-2-2-2-200000000-2-2-2-200000000000000-2-2000000002002002200000000000000
χ4322222222-2-22-2-2222-2-2-2-222220000-2-22200000000-2-2-2-2-2-2222200000000-2-2-2-2000000000000002200000000-200-2002200000000000000
χ4422222222-2-22-2-2222-2-2-2-222220000-2-22200000000-2-2-2-2-2-2-2-2-2-2000000002222000000000000002200000000200200-2-200000000000000
χ452222-2-2-2-2222-2-22222i2i−2i−2i-2-2-2-2000022−2i2i00000000-2-22i2i−2i−2i22-2-2000000002i2i−2i−2i00000000000000−2i2i00000000200-200−2i2i00000000000000
χ462222-2-2-2-2222-2-22222i2i−2i−2i-2-2-2-2000022−2i2i00000000-2-22i2i−2i−2i-2-22200000000−2i−2i2i2i00000000000000−2i2i00000000-2002002i−2i00000000000000
χ472222-2-2-2-2222-2-2222−2i−2i2i2i-2-2-2-20000222i−2i00000000-2-2−2i−2i2i2i22-2-200000000−2i−2i2i2i000000000000002i−2i00000000200-2002i−2i00000000000000
χ482222-2-2-2-2222-2-2222−2i−2i2i2i-2-2-2-20000222i−2i00000000-2-2−2i−2i2i2i-2-222000000002i2i−2i−2i000000000000002i−2i00000000-200200−2i2i00000000000000
χ492222-2-2-2-2-2-2-122-1-1-12i2i−2i−2i11112i2i−2i−2i112i−2i2i2i−2i−2i22-2-2-1-1−i−iii000000000000000022-2-2-1-12i−2i11−i−iii−ii−i−iii-1-111000000000000-11−ii000000
χ502222-2-2-2-2-2-2-122-1-1-12i2i−2i−2i11112i2i−2i−2i112i−2i−2i−2i2i2i22-2-2-1-1−i−iii0000000000000000-2-22211−2i2i-1-1−i−iii−iiii−i−i-1-1110000000000001-1i−i000000
χ512222-2-2-2-2-2-2-122-1-1-12i2i−2i−2i1111−2i−2i2i2i112i−2i2i2i−2i−2i-2-222-1-1−i−iii00000000000000002-2-22-1-1−2i2i11ii−i−i−ii−i−iii11-1-10000000000001-1i−i000000
χ522222-2-2-2-2-2-2-122-1-1-12i2i−2i−2i1111−2i−2i2i2i112i−2i−2i−2i2i2i-2-222-1-1−i−iii0000000000000000-222-2112i−2i-1-1ii−i−i−iiii−i−i11-1-1000000000000-11−ii000000
χ532222-2-2-2-2-2-2-122-1-1-1−2i−2i2i2i11112i2i−2i−2i11−2i2i2i2i−2i−2i-2-222-1-1ii−i−i0000000000000000-222-211−2i2i-1-1−i−iiii−i−i−iii11-1-1000000000000-11i−i000000
χ542222-2-2-2-2-2-2-122-1-1-1−2i−2i2i2i11112i2i−2i−2i11−2i2i−2i−2i2i2i-2-222-1-1ii−i−i00000000000000002-2-22-1-12i−2i11−i−iiii−iii−i−i11-1-10000000000001-1−ii000000
χ552222-2-2-2-2-2-2-122-1-1-1−2i−2i2i2i1111−2i−2i2i2i11−2i2i2i2i−2i−2i22-2-2-1-1ii−i−i0000000000000000-2-222112i−2i-1-1ii−i−ii−i−i−iii-1-1110000000000001-1−ii000000
χ562222-2-2-2-2-2-2-122-1-1-1−2i−2i2i2i1111−2i−2i2i2i11−2i2i−2i−2i2i2i22-2-2-1-1ii−i−i000000000000000022-2-2-1-1−2i2i11ii−i−ii−iii−i−i-1-111000000000000-11i−i000000
χ5722-2-22i−2i2i−2i002002-2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i1+i−1−i1−i−1+i000000002−2−i2i2002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000001+i−1−i1−i−1+i0000002−2−i2i2000000002−2−i2i20000000000
χ5822-2-22i−2i2i−2i002002-2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i1+i−1−i1−i−1+i000000002−2−i2i2002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-22−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000001+i−1−i1−i−1+i0000002−2−i2i200000000−22i2−i20000000000
χ5922-2-22i−2i2i−2i002002-2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i−1−i1+i−1+i1−i00000000−22i2−i2002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132-22i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000−1−i1+i−1+i1−i000000−22i2−i200000000−22i2−i20000000000
χ6022-2-22i−2i2i−2i002002-2-22ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132i−2i2i−2i−1−i1+i−1+i1−i00000000−22i2−i2002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13-22−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000−1−i1+i−1+i1−i000000−22i2−i2000000002−2−i2i20000000000
χ6122-2-22i−2i2i−2i002002-2-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i2i−2i1+i−1−i1−i−1+i00000000−22i2−i200−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000001+i−1−i1−i−1+i000000−22i2−i200000000−22i2−i20000000000
χ6222-2-22i−2i2i−2i002002-2-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i2i−2i1+i−1−i1−i−1+i00000000−22i2−i200−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-22−2i2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000001+i−1−i1−i−1+i000000−22i2−i2000000002−2−i2i20000000000
χ6322-2-22i−2i2i−2i002002-2-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i2i−2i−1−i1+i−1+i1−i000000002−2−i2i200−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132-22i−2i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000−1−i1+i−1+i1−i0000002−2−i2i2000000002−2−i2i20000000000
χ6422-2-22i−2i2i−2i002002-2-2−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132i−2i2i−2i−1−i1+i−1+i1−i000000002−2−i2i200−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13-22−2i2i1+i1+i−1−i−1−i1−i1−i−1+i−1+i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000−1−i1+i−1+i1−i0000002−2−i2i200000000−22i2−i20000000000
χ6522-2-2−2i2i−2i2i002002-2-2−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23−2i2i−2i2i1−i−1+i1+i−1−i000000002−2i2−i200−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232-2−2i2i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000001−i−1+i1+i−1−i0000002−2i2−i2000000002−2i2−i20000000000
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χ1078-88-88i−8i−8i8i00-4004-440000−4i4i4i−4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8−8i8i8i−8i00-4004-4400004i−4i−4i4i000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.