Finite Group Databasebeta

← Group #13155586

Character table — Group #13155586

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size1111111122222222222222222222222244444444444444444444444466666666666666666666666688888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order1222444433366666666612121212121212121212121233366666666612121212121212121212121222446666888812121212242424242424242436661212121266666688121212121212242424242424242424242424242424242424242424242424242424248888242424242424242424668812122424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
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−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii−i−iiiii−i−i−i−i1-111i−i-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-1-1-1-1-1-1ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiii−i−iiiii−i−i−i−i-11-1-1−ii11−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-1-1-1-1-1-1−i−iiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−iii−i−i−i−iiiii-11-1-1i−i11ii−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−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−i−i−iiiii1-111−ii-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−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iii−i−i−i−iiiii1-111−ii-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−ii111111ii−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−iii−i−i−i−iiiii-11-1-1i−i11ii−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−i111111−i−iiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iii−i−iiiii−i−i−i−i-11-1-1−ii11−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−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiiiii−i−iiiii−i−i−i−i1-111i−i-1-1ii−i−i-11
χ172222222222-12222-1-122-12222-1-1-1-12222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-1000000002222000022222222-1-1-1-1-1-1-1-100000022000000-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-100-1-1000000
χ182222222222-12222-1-122-12222-1-1-1-12222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-1000000002222000022222222-1-1-1-1-1-1-1-1000000-2-2000000-1-1-1-1-2-211-2-211-1-1-1-1-1-1-1-111111111000000000000-2-2110011000000
χ192222222222-12222-1-122-12222-1-1-1-12222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-100000000-2-2-2-20000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000022000000111122-1-122-1-111111111-1-1-1-1-1-1-1-1000000000000-2-2110011000000
χ202222222222-12222-1-122-12222-1-1-1-12222-1-12-1-1-1-122-1-12-1-1-1-12222-1-1-1-100000000-2-2-2-20000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000-2-20000001111-2-211-2-211111111111111111100000000000022-1-100-1-1000000
χ21222222222-1222-1-1222-1222-1-12222-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1222222220000222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-10000-1-122-1-12200000000-1-1-1-1-1-1-1-100000000000000002200-1-1-1-100
χ22222222222-1222-1-1222-1222-1-12222-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1222222220000222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-1-1-1-1-1-1000011-2-211-2-200000000111111110000000000000000-2-200111100
χ23222222222-1222-1-1222-1222-1-12222-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-20000-2-2-2-200000000-1-1-1-1-1-1-1-1111111221111110000-1-122-1-12200000000-1-1-1-1-1-1-1-10000000000000000-2-200111100
χ24222222222-1222-1-1222-1222-1-12222-1-1222-1-122-1-1-1-12-1-122-1-1-1-1-1-122-1-1-2-2-2-2-2-2-2-20000-2-2-2-200000000-1-1-1-1-1-1-1-1111111-2-2111111000011-2-211-2-2000000001111111100000000000000002200-1-1-1-100
χ2522222222-122-1-12222-122-1-122222222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-10022-1-1-1-1222200000000-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000000000
χ2622222222-122-1-12222-122-1-122222222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-1-1-1-111111111-1-1-1-1-1-1-1-122-1-1-1-10022-1-1-1-1-2-2-2-2000000001111111100000000-2-2-2-21111111100000000000000
χ2722222222-122-1-12222-122-1-122222222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122-2-2-2-2111122221111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2111100-2-21111222200000000-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000000000
χ2822222222-122-1-12222-122-1-122222222-1-1-12-1-1-122-1-1-12-1-1-122-1-1-1-1-1-122-2-2-2-21111-2-2-2-2111111111111-1-1-1-1-1-1-1-1-2-2111100-2-21111-2-2-2-20000000011111111000000002222-1-1-1-1-1-1-1-100000000000000
χ292222-2-2-2-222-12222-1-122-1-2-2-2-21111-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-21111000000002i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i-1-1-1-111110000002i−2i000000−i−iii2i2i−i−i−2i−2iii−i−i−i−iiiii−i−i−i−iiiii0000000000002-2-1-10011000000
χ302222-2-2-2-222-12222-1-122-1-2-2-2-21111-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-21111000000002i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i-1-1-1-11111000000−2i2i000000−i−iii−2i−2iii2i2i−i−i−i−i−i−iiiiiiiii−i−i−i−i000000000000-221100-1-1000000
χ312222-2-2-2-222-12222-1-122-1-2-2-2-21111-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-2111100000000−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i-1-1-1-111110000002i−2i000000ii−i−i2i2i−i−i−2i−2iiiiiii−i−i−i−i−i−i−i−iiiii000000000000-221100-1-1000000
χ322222-2-2-2-222-12222-1-122-1-2-2-2-21111-2-2-2-2-1-12-1-1-1-122-1-121111-2-2-2-2111100000000−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i-1-1-1-11111000000−2i2i000000ii−i−i−2i−2iii2i2i−i−iiiii−i−i−i−iiiii−i−i−i−i0000000000002-2-1-10011000000
χ332222-2-2-2-22-1222-1-1222-12-2-211-2-2-2-211-2-22-1-122-1-1-1-12-1-1-2-2111111-2-21122-2-222220000-2-2-2-200000000-1-1-1-11111-1-1-1-1-1-12i−2i1111110000−i−i2i2iii−2i−2i00000000−i−i−i−iiiii00000000000000002i−2i00−i−iii00
χ342222-2-2-2-22-1222-1-1222-12-2-211-2-2-2-211-2-22-1-122-1-1-1-12-1-1-2-2111111-2-21122-2-222220000-2-2-2-200000000-1-1-1-11111-1-1-1-1-1-1−2i2i1111110000ii−2i−2i−i−i2i2i00000000iiii−i−i−i−i0000000000000000−2i2i00ii−i−i00
χ352222-2-2-2-22-1222-1-1222-12-2-211-2-2-2-211-2-22-1-122-1-1-1-12-1-1-2-2111111-2-211-2-222-2-2-2-20000222200000000-1-1-1-111111111112i−2i-1-1-1-1-1-10000−i−i2i2iii−2i−2i00000000−i−i−i−iiiii0000000000000000−2i2i00ii−i−i00
χ362222-2-2-2-22-1222-1-1222-12-2-211-2-2-2-211-2-22-1-122-1-1-1-12-1-1-2-2111111-2-211-2-222-2-2-2-20000222200000000-1-1-1-11111111111−2i2i-1-1-1-1-1-10000ii−2i−2i−i−i2i2i00000000iiii−i−i−i−i00000000000000002i−2i00−i−iii00
χ372222-2-2-2-2-122-1-12222-12211-2-2-2-2-2-2-2-211-12-1-1-122-1-1-12-111-2-2111111-2-222-2-2-1-1-1-12i2i−2i−2i1111−i−i−i−iiiii-1-1-1-1111122-1-1-1-100-2-211112i2i−2i−2i00000000−i−i−i−iiiii000000002i2i−2i−2i−i−i−i−iiiii00000000000000
χ382222-2-2-2-2-122-1-12222-12211-2-2-2-2-2-2-2-211-12-1-1-122-1-1-12-111-2-2111111-2-222-2-2-1-1-1-1−2i−2i2i2i1111iiii−i−i−i−i-1-1-1-1111122-1-1-1-100-2-21111−2i−2i2i2i00000000iiii−i−i−i−i00000000−2i−2i2i2iiiii−i−i−i−i00000000000000
χ392222-2-2-2-2-122-1-12222-12211-2-2-2-2-2-2-2-211-12-1-1-122-1-1-12-111-2-2111111-2-2-2-22211112i2i−2i−2i-1-1-1-1−i−i−i−iiiii-1-1-1-11111-2-211110022-1-1-1-12i2i−2i−2i00000000−i−i−i−iiiii00000000−2i−2i2i2iiiii−i−i−i−i00000000000000
χ402222-2-2-2-2-122-1-12222-12211-2-2-2-2-2-2-2-211-12-1-1-122-1-1-12-111-2-2111111-2-2-2-2221111−2i−2i2i2i-1-1-1-1iiii−i−i−i−i-1-1-1-11111-2-211110022-1-1-1-1−2i−2i2i2i00000000iiii−i−i−i−i000000002i2i−2i−2i−i−i−i−iiiii00000000000000
χ4122-2-222-2-2222-2-2-2-2-2-2222222222-2-2-2-2-2-2222-2-2-2-2-2-222222-2-222-2-2-2-2220000000000000000000000002-2-2222-2-20000000000000000000000000000000000000000002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000
χ4222-2-222-2-2222-2-2-2-2-2-2222222222-2-2-2-2-2-2222-2-2-2-2-2-222222-2-222-2-2-2-2220000000000000000000000002-2-2222-2-2000000000000000000000000000000000000000000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i00000000000000
χ4322-2-222-2-2-12211-2-2-2-2-122-1-12222-2-2-2-211-12-111-2-211-12-1-1-1-2-2-1-11111220000−i3−i3i3i30000−i3−i3i3i333−3−333−3−3-111-1-1-11100−i3−i3i3i30000−i3−i3i3i300000000000033−3−333−3−3000000002i−2i2i−2i−i−iii−i−iii00000000000000
χ4422-2-222-2-2-12211-2-2-2-2-122-1-12222-2-2-2-211-12-111-2-211-12-1-1-1-2-2-1-11111220000−i3−i3i3i30000−i3−i3i3i3−3−333−3−333-111-1-1-11100−i3−i3i3i30000−i3−i3i3i3000000000000−3−333−3−33300000000−2i2i−2i2iii−i−iii−i−i00000000000000
χ4522-2-222-2-2-12211-2-2-2-2-122-1-12222-2-2-2-211-12-111-2-211-12-1-1-1-2-2-1-11111220000i3i3−i3−i30000i3i3−i3−i333−3−333−3−3-111-1-1-11100i3i3−i3−i30000i3i3−i3−i300000000000033−3−333−3−300000000−2i2i−2i2iii−i−iii−i−i00000000000000
χ4622-2-222-2-2-12211-2-2-2-2-122-1-12222-2-2-2-211-12-111-2-211-12-1-1-1-2-2-1-11111220000i3i3−i3−i30000i3i3−i3−i3−3−333−3−333-111-1-1-11100i3i3−i3−i30000i3i3−i3−i3000000000000−3−333−3−333000000002i−2i2i−2i−i−iii−i−iii00000000000000
χ4722-2-2-2-222222-2-2-2-2-2-2222-2-2-2-2-2-2222222222-2-2-2-2-2-2222-2-222-2-22222-2-20000000000000000000000002-2-22-2-2220000000000000000000000000000000000000000002-2-2222-2-2-2-22200000000000000
χ4822-2-2-2-222222-2-2-2-2-2-2222-2-2-2-2-2-2222222222-2-2-2-2-2-2222-2-222-2-22222-2-20000000000000000000000002-2-22-2-222000000000000000000000000000000000000000000-222-2-2-22222-2-200000000000000
χ4922-2-2-2-222-12211-2-2-2-2-12211-2-2-2-22222-1-1-12-111-2-211-12-1112211-1-1-1-1-2-20000−i3−i3i3i30000i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3-111-111-1-100−i3−i3i3i30000i3i3−i3−i3000000000000−i3−i3i3i3i3i3−i3−i3000000002-2-22-1-11111-1-100000000000000
χ5022-2-2-2-222-12211-2-2-2-2-12211-2-2-2-22222-1-1-12-111-2-211-12-1112211-1-1-1-1-2-20000−i3−i3i3i30000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3-111-111-1-100−i3−i3i3i30000i3i3−i3−i3000000000000i3i3−i3−i3−i3−i3i3i300000000-222-211-1-1-1-11100000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.