Finite Group Databasebeta

← Group #13155584

Character table — Group #13155584

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size1111111122222222222222222222222244444444444444444444444466666666666666666666666688888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order122244443336666666661212121212121212121212123336666666661212121212121212121212122244666688881212121224242424242424243666121212126666668812121212121224242424242424242424242424242424242424242424242424242424888824242424242424244488121212122424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
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−i1111-1-1-1-1111111i−i-1-1-1-1-1-1ii−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i1-1i−i11-1-1ii−i−i1-1
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−i1111-1-1-1-1111111−ii-1-1-1-1-1-1−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiiiii−i−iiiii−i−i−i−i-11−ii-1-111−i−iii-11
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−iiiii1111-1-1-1-1111111i−i-1-1-1-1-1-1ii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii−i−i−i−iiiii-11i−i-1-111ii−i−i-11
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−iiiii1111-1-1-1-1111111−ii-1-1-1-1-1-1−i−iii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii1-1−ii11-1-1−i−iii1-1
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−i1111-1-1-1-1-1-1-1-1-1-1i−i111111ii−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii1-1−ii11-1-1−i−iii-11
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−i1111-1-1-1-1-1-1-1-1-1-1−ii111111−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−iii−i−i−i−iiiii-11i−i-1-111ii−i−i1-1
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−iiiii1111-1-1-1-1-1-1-1-1-1-1i−i111111ii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−iiiii−i−i−i−i-11−ii-1-111−i−iii1-1
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−iiiii1111-1-1-1-1-1-1-1-1-1-1−ii111111−i−iii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiiiii−i−iiiii−i−i−i−i1-1i−i11-1-1ii−i−i-11
χ172222222222-122-1-122-1222222-1-122-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1222222220000222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-100000000000000220000-1-1-1-100
χ182222222222-122-1-122-1222222-1-122-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1222222220000222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-1-1-1-1-1-111110000-2-2-2-2000000001111111100000000000000-2-20000111100
χ192222222222-122-1-122-1222222-1-122-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-20000-2-2-2-200000000-1-1-1-1-1-1-1-111111122111111-1-1-1-10000222200000000-1-1-1-1-1-1-1-100000000000000-2-20000111100
χ202222222222-122-1-122-1222222-1-122-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-20000-2-2-2-200000000-1-1-1-1-1-1-1-1111111-2-211111111110000-2-2-2-2000000001111111100000000000000220000-1-1-1-100
χ21222222222-12-1-1222-122222-1-1222222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10022-1-1-1-1000022220000-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000000000
χ22222222222-12-1-1222-122222-1-1222222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-122-1-1-1-10022-1-1-1-10000-2-2-2-200001111111100000000-2-2-2-21111111100000000000000
χ23222222222-12-1-1222-122222-1-1222222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122-2-2-2-2111122221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2111100-2-21111000022220000-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000000000
χ24222222222-12-1-1222-122222-1-1222222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122-2-2-2-21111-2-2-2-2111111111111-1-1-1-1-1-1-1-1-2-2111100-2-211110000-2-2-2-2000011111111000000002222-1-1-1-1-1-1-1-100000000000000
χ2522222222-1222222-122-1-1-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-1000000002222000022222222-1-1-1-1-1-1-1-1000000220000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002200-1-1-1-1000000
χ2622222222-1222222-122-1-1-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-1000000002222000022222222-1-1-1-1-1-1-1-1000000-2-2000000-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111000000000000-2-2001111000000
χ2722222222-1222222-122-1-1-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-100000000-2-2-2-20000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-10000002200000022221111-1-1-1-111111111-1-1-1-1-1-1-1-1000000000000-2-2001111000000
χ2822222222-1222222-122-1-1-1-12222-1-12222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-100000000-2-2-2-20000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000-2-2000000-2-2-2-21111111111111111111111110000000000002200-1-1-1-1000000
χ292222-2-2-2-222-122-1-122-122-2-2-2-211-2-211-2-22-1-122-1-1-1-12-1-1-2-2111111-2-21122-2-222220000-2-2-2-200000000-1-1-1-11111-1-1-1-1-1-12i−2i111111−i−iii00002i2i−2i−2i00000000−i−i−i−iiiii000000000000002i−2i0000−i−iii00
χ302222-2-2-2-222-122-1-122-122-2-2-2-211-2-211-2-22-1-122-1-1-1-12-1-1-2-2111111-2-21122-2-222220000-2-2-2-200000000-1-1-1-11111-1-1-1-1-1-1−2i2i111111ii−i−i0000−2i−2i2i2i00000000iiii−i−i−i−i00000000000000−2i2i0000ii−i−i00
χ312222-2-2-2-222-122-1-122-122-2-2-2-211-2-211-2-22-1-122-1-1-1-12-1-1-2-2111111-2-211-2-222-2-2-2-20000222200000000-1-1-1-111111111112i−2i-1-1-1-1-1-1−i−iii00002i2i−2i−2i00000000−i−i−i−iiiii00000000000000−2i2i0000ii−i−i00
χ322222-2-2-2-222-122-1-122-122-2-2-2-211-2-211-2-22-1-122-1-1-1-12-1-1-2-2111111-2-211-2-222-2-2-2-20000222200000000-1-1-1-11111111111−2i2i-1-1-1-1-1-1ii−i−i0000−2i−2i2i2i00000000iiii−i−i−i−i000000000000002i−2i0000−i−iii00
χ332222-2-2-2-22-12-1-1222-1222-2-211-2-2-2-2-2-211-12-1-1-122-1-1-12-111-2-2111111-2-222-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii-1-1-1-1111122-1-1-1-100-2-2111100002i2i−2i−2i0000−i−i−i−iiiii000000002i2i−2i−2i−i−i−i−iiiii00000000000000
χ342222-2-2-2-22-12-1-1222-1222-2-211-2-2-2-2-2-211-12-1-1-122-1-1-12-111-2-2111111-2-222-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i-1-1-1-1111122-1-1-1-100-2-211110000−2i−2i2i2i0000iiii−i−i−i−i00000000−2i−2i2i2iiiii−i−i−i−i00000000000000
χ352222-2-2-2-22-12-1-1222-1222-2-211-2-2-2-2-2-211-12-1-1-122-1-1-12-111-2-2111111-2-2-2-22211112i2i−2i−2i-1-1-1-1−i−i−i−iiiii-1-1-1-11111-2-211110022-1-1-1-100002i2i−2i−2i0000−i−i−i−iiiii00000000−2i−2i2i2iiiii−i−i−i−i00000000000000
χ362222-2-2-2-22-12-1-1222-1222-2-211-2-2-2-2-2-211-12-1-1-122-1-1-12-111-2-2111111-2-2-2-2221111−2i−2i2i2i-1-1-1-1iiii−i−i−i−i-1-1-1-11111-2-211110022-1-1-1-10000−2i−2i2i2i0000iiii−i−i−i−i000000002i2i−2i−2i−i−i−i−iiiii00000000000000
χ372222-2-2-2-2-1222222-122-1-111-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-21111000000002i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i-1-1-1-111110000002i−2i0000002i2i−2i−2i−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii0000000000002-200-1-111000000
χ382222-2-2-2-2-1222222-122-1-111-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-21111000000002i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i-1-1-1-11111000000−2i2i000000−2i−2i2i2i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i000000000000-220011-1-1000000
χ392222-2-2-2-2-1222222-122-1-111-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-2111100000000−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i-1-1-1-111110000002i−2i0000002i2i−2i−2iii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii000000000000-220011-1-1000000
χ402222-2-2-2-2-1222222-122-1-111-2-2-2-211-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-2111100000000−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i-1-1-1-11111000000−2i2i000000−2i−2i2i2iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i0000000000002-200-1-111000000
χ4122-2-22i−2i2i−2i2222-22-2-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1322-2-22i2i−2i−2i0000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ130000000000000000000000000000000000
χ4222-2-22i−2i2i−2i2222-22-2-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i2i−2i−2i2i−2i2i−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1322-2-22i2i−2i−2i000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ130000000000000000000000000000000000
χ4322-2-22i−2i2i−2i2-12-112-2-21-22-22i−2i−ii2i−2i2i−2i2i−2i−ii-12-1-112-2-111-21−ii2i−2i−i−iii−ii2i−2i0000−i3−i3i3i32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1333−3−3−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13-1-111−i−iii00−i3−i3i3i3000033−3−300002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13000000000000−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ1300000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.