Finite Group Databasebeta

← Group #13155567

Character table — Group #13155567

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size1111111122222222222222222222222244444444444444444444444466666666666666666666666688888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order1222444433366666666612121212121212121212121233366666666612121212121212121212121222446666888812121212242424242424242436661212121244666666121212121212121212121212121212121212121212122424242424242424242424248888242424242424242424668812122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-111111111-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i1111-1-1-1-11-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1ii−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i1-111i−i-1-1ii−i−ii−i
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i1111-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1ii−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i-11-1-1−ii11−i−iii−ii
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii-1-1-1-1−i−i−i−iiiii1111-1-1-1-11-11111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−iii−i−i−i−iiiii−i−iii−i−i−i−iiiii1-111−ii-1-1−i−iii−ii
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii-1-1-1-1−i−i−i−iiiii1111-1-1-1-1-11111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1−i−iii−i−i−i−iiiii−i−iii−i−i−i−iiiii-11-1-1i−i11ii−i−ii−i
χ131111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i1111-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111ii−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii-11-1-1i−i11ii−i−i−ii
χ141111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1ii−i−i1111iiii−i−i−i−i1111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111ii−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii1-111−ii-1-1−i−iiii−i
χ151111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii1111-1-1-1-11-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111−i−iii−i−i−i−iiiiiii−i−iiiii−i−i−i−i-11-1-1−ii11−i−iiii−i
χ161111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1−i−iii1111−i−i−i−iiiii1111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111−i−iii−i−i−i−iiiiiii−i−iiiii−i−i−i−i1-111i−i-1-1ii−i−i−ii
χ172222222222-122222-1-12-122-1-1-1-12222222-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-122222222220000222200000000-1-1-1-1-1-1-1-122-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000022-1-100-1-1000000
χ182222222222-122222-1-12-122-1-1-1-12222222-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-122222222220000222200000000-1-1-1-1-1-1-1-1-2-2-1-1-1-1-1-1-2-211-2-211-1-111111111-1-1-1-1000000000000000000000000-2-2110011000000
χ192222222222-122222-1-12-122-1-1-1-12222222-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-20000-2-2-2-200000000-1-1-1-1-1-1-1-12211111122-1-122-1-111-1-1-1-1-1-1-1-11111000000000000000000000000-2-2110011000000
χ202222222222-122222-1-12-122-1-1-1-12222222-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-20000-2-2-2-200000000-1-1-1-1-1-1-1-1-2-2111111-2-211-2-2111111111111111100000000000000000000000022-1-100-1-1000000
χ21222222222-12-1-122222-12-1-122222222-1-1-12-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022-1-1-1-1000000002200000000-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ22222222222-12-1-122222-12-1-122222222-1-1-12-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-12222-1-1-1-1-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-10022-1-1-1-1000000002200000000-1-1-1-1-2-2-2-211111111-2-2-2-21111111100000000000000
χ23222222222-12-1-122222-12-1-122222222-1-1-12-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-2-2-2-2111122221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2111100000000-2-20000000011112222-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ24222222222-12-1-122222-12-1-122222222-1-1-12-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-2-2-2-21111-2-2-2-2111111111111-1-1-1-1-1-1-1-100-2-2111100000000-2-2000000001111-2-2-2-2111111112222-1-1-1-1-1-1-1-100000000000000
χ2522222222-12222-1-1-12222222222-1-1-1-122-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-1000000002222000022222222-1-1-1-1-1-1-1-122000000-1-122-1-12200-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-100000000000000002200-1-1-1-100
χ2622222222-12222-1-1-12222222222-1-1-1-122-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-1000000002222000022222222-1-1-1-1-1-1-1-1-2-200000011-2-211-2-200111111110000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-200111100
χ2722222222-12222-1-1-12222222222-1-1-1-122-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-100000000-2-2-2-20000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-122000000-1-122-1-12200-1-1-1-1-1-1-1-100001111111111110000000000000000-2-200111100
χ2822222222-12222-1-1-12222222222-1-1-1-122-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-100000000-2-2-2-20000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-200000011-2-211-2-20011111111000011111111111100000000000000002200-1-1-1-100
χ292222-2-2-2-222-122222-1-12-1-2-21111-2-2-2-2-2-22-1-122-1-12-1-1-1-1-2-211111111-2-222-2-222220000-2-2-2-200000000-1-1-1-111112-2-1-1-1-1-1-122-1-1-2-21111-1-1-1-1111111110000000000000000000000002-2-1-10011000000
χ302222-2-2-2-222-122222-1-12-1-2-21111-2-2-2-2-2-22-1-122-1-12-1-1-1-1-2-211111111-2-222-2-222220000-2-2-2-200000000-1-1-1-11111-22-1-1-1-1-1-1-2-21122-1-1111111-1-1-1-11111000000000000000000000000-221100-1-1000000
χ312222-2-2-2-222-122222-1-12-1-2-21111-2-2-2-2-2-22-1-122-1-12-1-1-1-1-2-211111111-2-2-2-222-2-2-2-20000222200000000-1-1-1-111112-211111122-1-1-2-211-1-1-1-1-1-11111-1-1-1-1000000000000000000000000-221100-1-1000000
χ322222-2-2-2-222-122222-1-12-1-2-21111-2-2-2-2-2-22-1-122-1-12-1-1-1-1-2-211111111-2-2-2-222-2-2-2-20000222200000000-1-1-1-11111-22111111-2-21122-1-1-1-11111-1-1-1-1-1-1-1-10000000000000000000000002-2-1-10011000000
χ332222-2-2-2-22-12-1-122222-1211-2-2-2-2-2-2-2-211-12-1-1-1-1-1-1222-111-2-2-2-211111122-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii-1-1-1-111110022-1-1-1-100000000-2-20000000011112i2i−2i−2i−i−i−i−iiiii2i2i−2i−2i−i−i−i−iiiii00000000000000
χ342222-2-2-2-22-12-1-122222-1211-2-2-2-2-2-2-2-211-12-1-1-1-1-1-1222-111-2-2-2-211111122-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i-1-1-1-111110022-1-1-1-100000000-2-2000000001111−2i−2i2i2iiiii−i−i−i−i−2i−2i2i2iiiii−i−i−i−i00000000000000
χ352222-2-2-2-22-12-1-122222-1211-2-2-2-2-2-2-2-211-12-1-1-1-1-1-1222-111-2-2-2-2111111-2-22211112i2i−2i−2i-1-1-1-1−i−i−i−iiiii-1-1-1-1111100-2-21111000000002200000000-1-1-1-12i2i−2i−2i−i−i−i−iiiii−2i−2i2i2iiiii−i−i−i−i00000000000000
χ362222-2-2-2-22-12-1-122222-1211-2-2-2-2-2-2-2-211-12-1-1-1-1-1-1222-111-2-2-2-2111111-2-2221111−2i−2i2i2i-1-1-1-1iiii−i−i−i−i-1-1-1-1111100-2-21111000000002200000000-1-1-1-1−2i−2i2i2iiiii−i−i−i−i2i2i−2i−2i−i−i−i−iiiii00000000000000
χ372222-2-2-2-2-12222-1-1-12222-2-2-2-2-2-21111-2-2-1-12-1-122-1-1-1-12111111-2-2-2-211000000002i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i-1-1-1-111112-2000000-1-12211-2-200-1-1-1-111110000−i−iii−i−i−i−iiiii00000000000000002i−2i00−i−iii00
χ382222-2-2-2-2-12222-1-1-12222-2-2-2-2-2-21111-2-2-1-12-1-122-1-1-1-12111111-2-2-2-211000000002i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i-1-1-1-11111-2200000011-2-2-1-122001111-1-1-1-10000−i−iii−i−i−i−iiiii0000000000000000−2i2i00ii−i−i00
χ392222-2-2-2-2-12222-1-1-12222-2-2-2-2-2-21111-2-2-1-12-1-122-1-1-1-12111111-2-2-2-21100000000−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i-1-1-1-111112-2000000-1-12211-2-200-1-1-1-111110000ii−i−iiiii−i−i−i−i0000000000000000−2i2i00ii−i−i00
χ402222-2-2-2-2-12222-1-1-12222-2-2-2-2-2-21111-2-2-1-12-1-122-1-1-1-12111111-2-2-2-21100000000−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i-1-1-1-11111-2200000011-2-2-1-122001111-1-1-1-10000ii−i−iiiii−i−i−i−i00000000000000002i−2i00−i−iii00
χ4122-2-22i−2i2i−2i2222-2-22-22-2-2-22i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2222-22-2-2-22-2-22i−2i2i2i−2i−2i2i2i−2i−2i2i−2i00000000000000000000000022-2-22i2i−2i−2i0000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300000000000000
χ4222-2-22i−2i2i−2i2222-2-22-22-2-2-22i−2i2i2i−2i−2i2i−2i2i−2i2i−2i2222-22-2-2-22-2-22i−2i2i2i−2i−2i2i2i−2i−2i2i−2i00000000000000000000000022-2-22i2i−2i−2i000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300000000000000
χ4322-2-22i−2i2i−2i2-12-11-22-22-21-2−ii2i2i−2i−2i2i−2i2i−2i−ii-12-1-11-111-22-21−ii2i2i−2i−2i−i−iii−ii0000−i3−i3i3i3000033−3−3−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13-1-111−i−iii0000−i3−i3i3i300000000000000000033−3−30000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ132ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ1300000000000000
χ4422-2-22i−2i2i−2i2-12-11-22-22-21-2−ii2i2i−2i−2i2i−2i2i−2i−ii-12-1-11-111-22-21−ii2i2i−2i−2i−i−iii−ii0000−i3−i3i3i3000033−3−3ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13-1-111−i−iii0000−i3−i3i3i300000000000000000033−3−30000ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000000000
χ4522-2-22i−2i2i−2i2-12-11-22-22-21-2−ii2i2i−2i−2i2i−2i2i−2i−ii-12-1-11-111-22-21−ii2i2i−2i−2i−i−iii−ii0000i3i3−i3−i30000−3−333−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13-1-111−i−iii0000i3i3−i3−i3000000000000000000−3−3330000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ1300000000000000
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χ1454-4-44-4-444-24-2-4-4-222224-2-4-42-2-22-2-22244-21-22222-21-1-1-222-111-12-2-22-2-20000000000000000000000001-1-11-111-10000000023−2300−23230000−33−333−33−3000000000000000000000000000000000000000000
χ1464-4-44-4-444-24-2-4-4-222224-2-4-42-2-22-2-22244-21-22222-21-1-1-222-111-12-2-22-2-20000000000000000000000001-1-11-111-100000000−23230023−2300003−33−3−33−33000000000000000000000000000000000000000000
χ1474-4-44-4-444-2-2422-222-4-4-2422-444-4-2-222-2-21-2-2-1-1221-222-2-1-12-2-222-2-2211000000004-4-440000-222-2-222-21-1-11-111-1000000000000000000000000000000-222-21-1-111-1-1100000000000000000000000000
χ1484-4-44-4-444-2-2422-222-4-4-2422-444-4-2-222-2-21-2-2-1-1221-222-2-1-12-2-222-2-221100000000-444-400002-2-222-2-221-1-11-111-10000000000000000000000000000002-2-22-111-1-111-100000000000000000000000000
χ14988888888-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4222222222222222222222222000000000000000000000000-1-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000000000000000
χ1508888-8-8-8-8-4-4-4-4-4-4-4-4-4-4-4-4444444444444222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000-1-1-1-1111100000000000000000000000000000000000000000000000000000000000000000000
χ15188-8-88i−8i8i−8i-4-4-4-444-44-4444−4i4i−4i−4i4i4i−4i4i−4i4i−4i4i2222-22-2-2-22-2-22i−2i2i2i−2i−2i2i2i−2i−2i2i−2i000000000000000000000000-1-111−i−iii00000000000000000000000000000000000000000000000000000000000000000000
χ15288-8-8−8i8i−8i8i-4-4-4-444-44-44444i−4i4i4i−4i−4i4i−4i4i−4i4i−4i2222-22-2-2-22-2-2−2i2i−2i−2i2i2i−2i−2i2i2i−2i2i000000000000000000000000-1-111ii−i−i00000000000000000000000000000000000000000000000000000000000000000000
χ1538-88-88i−8i−8i8i-4-4-44-444-44-444−4i4i−4i4i−4i4i4i−4i−4i4i4i−4i222-22-22-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i−2i2i000000000000000000000000-11-11−ii−ii00000000000000000000000000000000000000000000000000000000000000000000
χ1548-88-8−8i8i8i−8i-4-4-44-444-44-4444i−4i4i−4i4i−4i−4i4i4i−4i−4i4i222-22-22-2-2-22-2−2i2i−2i2i−2i2i−2i2i−2i2i2i−2i000000000000000000000000-11-11i−ii−i00000000000000000000000000000000000000000000000000000000000000000000
χ1558-8-8888-8-8-4-4-444-44444-4-4-4-4-444-444-4-444222-2-2-2-222-2-22222-2-222-2-22-2-2000000000000000000000000-111-1-111-100000000000000000000000000000000000000000000000000000000000000000000
χ1568-8-88-8-888-4-4-444-44444-4-4444-4-44-4-444-4-4222-2-2-2-222-2-22-2-2-222-2-222-222000000000000000000000000-111-11-1-1100000000000000000000000000000000000000000000000000000000000000000000

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