Finite Group Databasebeta

← Group #13155545

Character table — Group #13155545

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size1111111122222222222222222222222244444444444444444444444466666666666666666666666688888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order12224444333666666666121212121212121212121212333666666666121212121212121212121212888888882424242424242424242424242424242436661212121288242424242424242424242424242424242424242424242424242424242424242424242424242424244444121212121212121224446612121212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
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
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1i−iii−i−iii−i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-11-11-11111-1-1-1-1i−i
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−iiii−i−i−i−iiiii−i−i−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-11111-1-1-1-1-11-11-1-1-1-11111−ii
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1i−i−i−iiiii−i−iii−i−iii−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-11111-111-1-1-111-1-111−ii
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−ii−i−iii−i−iiiii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-111111-1-1111-1-111-1-1i−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−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1i−iii−i−iii−i−i−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-111111-1-1111-1-111-1-1−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−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−iiii−i−i−i−iii−i−iii−i−iii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-11111-111-1-1-111-1-111i−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−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1i−i−i−iiiii−i−i−i−iiiii−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-11111-1-1-1-1-11-11-1-1-1-11111i−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−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−ii−i−iii−i−iii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-11-11-11111-1-1-1-1−ii
χ172222222222-1-1-1222222-1222222-1-1-1-1222-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1000022220000000022222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000002200-1-10000-1-100
χ182222222222-1-1-1222222-1222222-1-1-1-1222-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-1000022220000000022222222-1-1-1-1-1-1-1-1-2-2-1-1-1-111110000-2-2-2-200000000-1-1-1-1-1-1-1-111111111000000000000-2-2001100001100
χ192222222222-1-1-1222222-1222222-1-1-1-1222-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1221111-1-1-1-1000022220000000011111111-1-1-1-1-1-1-1-1000000000000-2-2001100001100
χ202222222222-1-1-1222222-1222222-1-1-1-1222-1-122-1-1-1-12-1-122-1-1-1-122-1-1-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-2111111110000-2-2-2-20000000011111111111111110000000000002200-1-10000-1-100
χ21222222222-12222-122-1-1222-1-1-1-1222222-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002222000022220000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000000000
χ22222222222-12222-122-1-1222-1-1-1-1222222-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-100-2-2-2-2000022220000-1-1-1-1-1-1-1-11111111100000000-2-2-2-21111111100000000000000
χ23222222222-12222-122-1-1222-1-1-1-1222222-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022220000-2-2-2-2000011111111-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000000000
χ24222222222-12222-122-1-1222-1-1-1-1222222-12-1-1-122-1-1-12-1-1-122-1-1-1-122-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-100-2-2-2-20000-2-2-2-200001111111111111111000000002222-1-1-1-1-1-1-1-100000000000000
χ2522222222-12222-12-1-1222-1-122222222-1-1-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-122222200002222222200000000-1-1-1-1-1-1-1-12200002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1000000000000002200-1-1-1-10000
χ2622222222-12222-12-1-1222-1-122222222-1-1-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-122222200002222222200000000-1-1-1-1-1-1-1-1-2-20000-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1000000001111111100000000000000-2-20011110000
χ2722222222-12222-12-1-1222-1-122222222-1-1-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-122000022221111-1-1-1-11111111100000000-1-1-1-1-1-1-1-100000000000000-2-20011110000
χ2822222222-12222-12-1-1222-1-122222222-1-1-1-12-1-1-1-122-1-12-1-1-1-122-1-1-1-122-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-2-20000-2-2-2-211111111111111110000000011111111000000000000002200-1-1-1-10000
χ292222-2-2-2-222-1-1-1222222-1-2-2-2-2-2-21111-2-22-1-122-1-1-1-12-1-1-2-21111-2-2111100002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-1-1-1-111112i−2i−i−iii−i−iii00002i2i−2i−2i00000000−i−i−i−iiiii−i−i−i−iiiii0000000000002-200-1-100001100
χ302222-2-2-2-222-1-1-1222222-1-2-2-2-2-2-21111-2-22-1-122-1-1-1-12-1-1-2-21111-2-2111100002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-1-1-1-11111−2i2i−i−iiiii−i−i0000−2i−2i2i2i00000000−i−i−i−iiiiiiiii−i−i−i−i000000000000-2200110000-1-100
χ312222-2-2-2-222-1-1-1222222-1-2-2-2-2-2-21111-2-22-1-122-1-1-1-12-1-1-2-21111-2-211110000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i-1-1-1-111112i−2iii−i−i−i−iii00002i2i−2i−2i00000000iiii−i−i−i−i−i−i−i−iiiii000000000000-2200110000-1-100
χ322222-2-2-2-222-1-1-1222222-1-2-2-2-2-2-21111-2-22-1-122-1-1-1-12-1-1-2-21111-2-211110000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i-1-1-1-11111−2i2iii−i−iii−i−i0000−2i−2i2i2i00000000iiii−i−i−i−iiiii−i−i−i−i0000000000002-200-1-100001100
χ332222-2-2-2-22-12222-122-1-12-2-21111-2-2-2-2-2-2-12-1-1-122-1-1-12-111-2-21111-2-2112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii-1-1-1-11111002i2i−2i−2i00002i2i−2i−2i0000−i−i−i−iiiii−i−i−i−iiiii0000000022-2-2-1-1-1-1111100000000000000
χ342222-2-2-2-22-12222-122-1-12-2-21111-2-2-2-2-2-2-12-1-1-122-1-1-12-111-2-21111-2-2112i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-1111100−2i−2i2i2i00002i2i−2i−2i0000−i−i−i−iiiiiiiii−i−i−i−i00000000-2-2221111-1-1-1-100000000000000
χ352222-2-2-2-22-12222-122-1-12-2-21111-2-2-2-2-2-2-12-1-1-122-1-1-12-111-2-21111-2-211−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-11111002i2i−2i−2i0000−2i−2i2i2i0000iiii−i−i−i−i−i−i−i−iiiii00000000-2-2221111-1-1-1-100000000000000
χ362222-2-2-2-22-12222-122-1-12-2-21111-2-2-2-2-2-2-12-1-1-122-1-1-12-111-2-21111-2-211−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i-1-1-1-1111100−2i−2i2i2i0000−2i−2i2i2i0000iiii−i−i−i−iiiii−i−i−i−i0000000022-2-2-1-1-1-1111100000000000000
χ372222-2-2-2-2-12222-12-1-122211-2-2-2-2-2-2-2-211-1-12-1-1-1-122-1-121111-2-21111-2-22i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i00000000-1-1-1-111112i−2i00002i2i−2i−2i−i−iii−i−iii−i−i−i−iiiii00000000−i−i−i−iiiii000000000000002-200-1-1110000
χ382222-2-2-2-2-12222-12-1-122211-2-2-2-2-2-2-2-211-1-12-1-1-1-122-1-121111-2-21111-2-22i2i−2i−2i00002i2i2i2i−2i−2i−2i−2i00000000-1-1-1-11111−2i2i0000−2i−2i2i2i−i−iiiii−i−i−i−i−i−iiiii00000000iiii−i−i−i−i00000000000000-220011-1-10000
χ392222-2-2-2-2-12222-12-1-122211-2-2-2-2-2-2-2-211-1-12-1-1-1-122-1-121111-2-21111-2-2−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i00000000-1-1-1-111112i−2i00002i2i−2i−2iii−i−i−i−iiiiiii−i−i−i−i00000000−i−i−i−iiiii00000000000000-220011-1-10000
χ402222-2-2-2-2-12222-12-1-122211-2-2-2-2-2-2-2-211-1-12-1-1-1-122-1-121111-2-21111-2-2−2i−2i2i2i0000−2i−2i−2i−2i2i2i2i2i00000000-1-1-1-11111−2i2i0000−2i−2i2i2iii−i−iii−i−iiiii−i−i−i−i00000000iiii−i−i−i−i000000000000002-200-1-1110000
χ4122-2-222-2-2222-2-222-2-2-2-22-2-222-2-222-2-222222-2-2-2-2-2-2222-2-2-2-2222222-2-20000000000000000000000002-2-2222-2-20000000000000000000000000000000000000000002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i00000000000000
χ4222-2-222-2-2222-2-222-2-2-2-22-2-222-2-222-2-222222-2-2-2-2-2-2222-2-2-2-2222222-2-20000000000000000000000002-2-2222-2-2000000000000000000000000000000000000000000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i00000000000000
χ4322-2-222-2-22-12-2-22-1-2-2112-2-2-1-11122-2-222-12-111-2-211-12-111-2-2-1-1-1-1221100000000−i3−i3i3i3−i3−i3i3i333−3−333−3−3-111-1-1-111000000000000000000−i3−i3i3i3−i3−i3i3i333−3−333−3−3000000002i−2i2i−2i−i−iii−i−iii00000000000000
χ4422-2-222-2-22-12-2-22-1-2-2112-2-2-1-11122-2-222-12-111-2-211-12-111-2-2-1-1-1-1221100000000−i3−i3i3i3−i3−i3i3i3−3−333−3−333-111-1-1-111000000000000000000−i3−i3i3i3−i3−i3i3i3−3−333−3−33300000000−2i2i−2i2iii−i−iii−i−i00000000000000
χ4522-2-222-2-22-12-2-22-1-2-2112-2-2-1-11122-2-222-12-111-2-211-12-111-2-2-1-1-1-1221100000000i3i3−i3−i3i3i3−i3−i333−3−333−3−3-111-1-1-111000000000000000000i3i3−i3−i3i3i3−i3−i333−3−333−3−300000000−2i2i−2i2iii−i−iii−i−i00000000000000
χ4622-2-222-2-22-12-2-22-1-2-2112-2-2-1-11122-2-222-12-111-2-211-12-111-2-2-1-1-1-1221100000000i3i3−i3−i3i3i3−i3−i3−3−333−3−333-111-1-1-111000000000000000000i3i3−i3−i3i3i3−i3−i3−3−333−3−333000000002i−2i2i−2i−i−iii−i−iii00000000000000
χ4722-2-2-2-222222-2-222-2-2-2-2222-2-222-2-222-2-2222-2-2-2-2-2-22222222-2-2-2-2-2-2220000000000000000000000002-2-22-2-2220000000000000000000000000000000000000000002i−2i−2i2i2i2i−2i−2i−2i−2i2i2i00000000000000
χ4822-2-2-2-222222-2-222-2-2-2-2222-2-222-2-222-2-2222-2-2-2-2-2-22222222-2-2-2-2-2-2220000000000000000000000002-2-22-2-222000000000000000000000000000000000000000000−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i00000000000000
χ4922-2-2-2-2222-12-2-22-1-2-21122211-1-1-2-222-2-2-12-111-2-211-12-1-1-1221111-2-2-1-10000000033−3−3−3−333−i3−i3i3i3i3i3−i3−i3-111-111-1-100000000000000000033−3−3−3−333−i3−i3i3i3i3i3−i3−i300000000−2i2i2i−2iii−i−i−i−iii00000000000000
χ5022-2-2-2-2222-12-2-22-1-2-21122211-1-1-2-222-2-2-12-111-2-211-12-1-1-1221111-2-2-1-10000000033−3−3−3−333i3i3−i3−i3−i3−i3i3i3-111-111-1-100000000000000000033−3−3−3−333i3i3−i3−i3−i3−i3i3i3000000002i−2i−2i2i−i−iiiii−i−i00000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.