Finite Group Databasebeta

← Group #13155565

Character table — Group #13155565

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size1111111122222222222222222222222244444444444444444444444466668888888812121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363654545454
order122244443336666666661212121212121212121212123336666666661212121212121212121212122244366612121212246666666666666666881212121212121212121212121212121224242424242424242424242424242424888844881212121224242424242424248888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-111-1-111-1-1-1-1111111-1-111-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111111111-1-111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11111111111111111i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i1-1i−i11-1-1ii−i−iii−i−iii−i−i
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11-11111111111111111−ii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii1-1−ii11-1-1−i−iii−i−iii−i−iii
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1111-1-111-1-11111-1-1-1-1i−i-1-111-1-111-1-1-1-11111ii−i−iii−i−iiiii−i−i−i−i−i−iii-11i−i-1-111ii−i−i−i−iii−i−iii
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1111-1-111-1-11111-1-1-1-1−ii-1-111-1-111-1-1-1-11111−i−iii−i−iii−i−i−i−iiiiiii−i−i-11−ii-1-111−i−iiiii−i−iii−i−i
χ131111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-111-1-111-1-1-1-11111i−i11-1-111-1-11111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i-11−ii-1-111−i−iiiii−i−i−i−iii
χ141111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1-111-1-111-1-1-1-11111−ii11-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii-11i−i-1-111ii−i−i−i−iiiii−i−i
χ151111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1i−i1111111111111111ii−i−iii−i−iiiii−i−i−i−i−i−iii1-1−ii11-1-1−i−iii−i−iiiii−i−i
χ161111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−ii1111111111111111−i−iii−i−iii−i−i−i−iiiiiii−i−i1-1i−i11-1-1ii−i−iii−i−i−i−iii
χ172222222222-1222222-1-1-122-1-1-1-12222222-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1002222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000002200-1-1-1-1000000000000
χ182222222222-1222222-1-1-122-1-1-1-12222222-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-2-222-2-2-1-111-1-1-1-111110022-2-2-1-111-1-1-1-1111100000000000000000000-2-2001111000000000000
χ192222222222-1222222-1-1-122-1-1-1-12222222-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-122-2-22211-1-11111-1-1-1-100-2-22211-1-11111-1-1-1-100000000000000000000-2-2001111000000000000
χ202222222222-1222222-1-1-122-1-1-1-12222222-1-122-1-1-1-12-1-122-1-1-1-1-1-1-1-122-2-2-2-2-1-1-1-1-1-1-1-1-2-2-2-2-2-211111111111100-2-2-2-2111111111111000000000000000000002200-1-1-1-1000000000000
χ21222222222-1222-1-12-1222222222-1-1-1-122-12-1-1-122-1-1-12-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-1-1002200-1-1-1-1000022-1-1002200-1-1-1-10000-1-1-1-12222-1-1-1-1-1-1-1-1000000220000-1-1-1-100000000
χ22222222222-1222-1-12-1222222222-1-1-1-122-12-1-1-122-1-1-12-1-1-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-100-1-1002200-1-1-1-10000-2-2-1-1002200-1-1-1-100001111-2-2-2-211111111000000-2-20000111100000000
χ23222222222-1222-1-12-1222222222-1-1-1-122-12-1-1-122-1-1-12-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1001100-2-20011110000221100-2-20011110000-1-1-1-12222-1-1-1-1-1-1-1-1000000-2-20000111100000000
χ24222222222-1222-1-12-1222222222-1-1-1-122-12-1-1-122-1-1-12-1-1-12222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1001100-2-20011110000-2-21100-2-200111100001111-2-2-2-211111111000000220000-1-1-1-100000000
χ2522222222-122-1-122-12222-1-122222222-1-1-1-12-1-1-1-122-1-12-1-1-1-1-1-12222-1-10000-1-1-1-1-1-1-1-12200-1-100220000-1-1-1-12200-1-100220000-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222000000000000-1-1-1-10000
χ2622222222-122-1-122-12222-1-122222222-1-1-1-12-1-1-1-122-1-12-1-1-1-1-1-12222-1-10000-1-1-1-1-1-1-1-12200-1-100220000-1-1-1-1-2-200-1-100220000-1-1-1-1-2-2-2-2111111111111-2-2-2-200000000000011110000
χ2722222222-122-1-122-12222-1-122222222-1-1-1-12-1-1-1-122-1-12-1-1-1-1-1-12222-1-10000-1-1-1-1-1-1-1-1-2-2001100-2-20000111122001100-2-2000011112222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200000000000011110000
χ2822222222-122-1-122-12222-1-122222222-1-1-1-12-1-1-1-122-1-12-1-1-1-1-1-12222-1-10000-1-1-1-1-1-1-1-1-2-2001100-2-200001111-2-2001100-2-200001111-2-2-2-21111111111112222000000000000-1-1-1-10000
χ292222-2-2-2-222-1222222-1-1-1-2-21111-2-2-2-2-2-22-1-122-1-1-1-12-1-1-2-211111111-2-222-2-2-1-1-1-111112-22222-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-2111111111111000000000000000000002-200-1-111000000000000
χ302222-2-2-2-222-1222222-1-1-1-2-21111-2-2-2-2-2-22-1-122-1-1-1-12-1-1-2-211111111-2-222-2-2-1-1-1-11111-2222-2-2-1-111-1-1-1-1111100-2-22211-1-11111-1-1-1-100000000000000000000-220011-1-1000000000000
χ312222-2-2-2-222-1222222-1-1-1-2-21111-2-2-2-2-2-22-1-122-1-1-1-12-1-1-2-211111111-2-2-2-222-1-1-1-111112-2-2-22211-1-11111-1-1-1-10022-2-2-1-111-1-1-1-1111100000000000000000000-220011-1-1000000000000
χ322222-2-2-2-222-1222222-1-1-1-2-21111-2-2-2-2-2-22-1-122-1-1-1-12-1-1-2-211111111-2-2-2-222-1-1-1-11111-22-2-2-2-2111111111111002222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000002-200-1-111000000000000
χ332222-2-2-2-22-1222-1-12-1222-2-2-2-2-2-21111-2-2-12-1-1-122-1-1-12-111-2-2-2-211111122-2-2-1-1-1-1111100-1-1002200-1-1-1-100002i−2i1100-2-20011110000−i−iii2i2i−2i−2i−i−i−i−iiiii0000002i−2i0000−i−iii00000000
χ342222-2-2-2-22-1222-1-12-1222-2-2-2-2-2-21111-2-2-12-1-1-122-1-1-12-111-2-2-2-211111122-2-2-1-1-1-1111100-1-1002200-1-1-1-10000−2i2i1100-2-20011110000ii−i−i−2i−2i2i2iiiii−i−i−i−i000000−2i2i0000ii−i−i00000000
χ352222-2-2-2-22-1222-1-12-1222-2-2-2-2-2-21111-2-2-12-1-1-122-1-1-12-111-2-2-2-2111111-2-222-1-1-1-11111001100-2-200111100002i−2i-1-1002200-1-1-1-10000−i−iii2i2i−2i−2i−i−i−i−iiiii000000−2i2i0000ii−i−i00000000
χ362222-2-2-2-22-1222-1-12-1222-2-2-2-2-2-21111-2-2-12-1-1-122-1-1-12-111-2-2-2-2111111-2-222-1-1-1-11111001100-2-20011110000−2i2i-1-1002200-1-1-1-10000ii−i−i−2i−2i2i2iiiii−i−i−i−i0000002i−2i0000−i−iii00000000
χ372222-2-2-2-2-122-1-122-1222211-2-2-2-2-2-2-2-211-1-12-1-1-1-122-1-12111111-2-2-2-2110000-1-1-1-111112-200-1-100220000-1-1-1-12i−2i001100-2-2000011112i2i−2i−2i−i−iii−i−i−i−iiiii2i2i−2i−2i000000000000−i−iii0000
χ382222-2-2-2-2-122-1-122-1222211-2-2-2-2-2-2-2-211-1-12-1-1-1-122-1-12111111-2-2-2-2110000-1-1-1-111112-200-1-100220000-1-1-1-1−2i2i001100-2-200001111−2i−2i2i2iii−i−iiiii−i−i−i−i−2i−2i2i2i000000000000ii−i−i0000
χ392222-2-2-2-2-122-1-122-1222211-2-2-2-2-2-2-2-211-1-12-1-1-1-122-1-12111111-2-2-2-2110000-1-1-1-11111-22001100-2-2000011112i−2i00-1-100220000-1-1-1-12i2i−2i−2i−i−iii−i−i−i−iiiii−2i−2i2i2i000000000000ii−i−i0000
χ402222-2-2-2-2-122-1-122-1222211-2-2-2-2-2-2-2-211-1-12-1-1-1-122-1-12111111-2-2-2-2110000-1-1-1-11111-22001100-2-200001111−2i2i00-1-100220000-1-1-1-1−2i−2i2i2iii−i−iiiii−i−i−i−i2i2i−2i−2i000000000000−i−iii0000
χ4122-2-222-2-2222-2-2-2-2222-2-22222-2-2-2-222-2-2222-2-2-2-2-2-22222222-2-222-2-2-2-200002-2-2222-2-200000000000000000000000000000000000000000000000000002i−2i2i−2i0000000000002i−2i2i−2i0000
χ4222-2-222-2-2222-2-2-2-2222-2-22222-2-2-2-222-2-2222-2-2-2-2-2-22222222-2-222-2-2-2-200002-2-2222-2-20000000000000000000000000000000000000000000000000000−2i2i−2i2i000000000000−2i2i−2i2i0000
χ4322-2-222-2-2-12211-2-2-122-2-2-1-122-2-2-2-22211-1-121111-2-2-1-12-1-1-1-11122-2-2110000-111-1-1-1110000−i3i300000000−i3−i3i3i30000−i3i300000000−i3−i3i3i300003−33−333−3−333−3−32i−2i2i−2i000000000000−ii−ii0000
χ4422-2-222-2-2-12211-2-2-122-2-2-1-122-2-2-2-22211-1-121111-2-2-1-12-1-1-1-11122-2-2110000-111-1-1-1110000−i3i300000000−i3−i3i3i30000−i3i300000000−i3−i3i3i30000−33−33−3−333−3−333−2i2i−2i2i000000000000i−ii−i0000
χ4522-2-222-2-2-12211-2-2-122-2-2-1-122-2-2-2-22211-1-121111-2-2-1-12-1-1-1-11122-2-2110000-111-1-1-1110000i3−i300000000i3i3−i3−i30000i3−i300000000i3i3−i3−i300003−33−333−3−333−3−3−2i2i−2i2i000000000000i−ii−i0000
χ4622-2-222-2-2-12211-2-2-122-2-2-1-122-2-2-2-22211-1-121111-2-2-1-12-1-1-1-11122-2-2110000-111-1-1-1110000i3−i300000000i3i3−i3−i30000i3−i300000000i3i3−i3−i30000−33−33−3−333−3−3332i−2i2i−2i000000000000−ii−ii0000
χ4722-2-2-2-222222-2-2-2-2222-2-2-2-2-2-22222-2-222222-2-2-2-2-2-2222-2-2-2-222-2-2222200002-2-22-2-22200000000000000000000000000000000000000000000000000002-2-220000000000002-2-220000
χ4822-2-2-2-222222-2-2-2-2222-2-2-2-2-2-22222-2-222222-2-2-2-2-2-2222-2-2-2-222-2-2222200002-2-22-2-2220000000000000000000000000000000000000000000000000000-222-2000000000000-222-20000
χ4922-2-2-2-222-12211-2-2-122-2-211-2-22222-2-2-1-1-1-121111-2-2-1-121111-1-1-2-222-1-10000-111-111-1-10000−i3i300000000−i3−i3i3i30000i3−i300000000i3i3−i3−i30000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i32-2-22000000000000-111-10000
χ5022-2-2-2-222-12211-2-2-122-2-211-2-22222-2-2-1-1-1-121111-2-2-1-121111-1-1-2-222-1-10000-111-111-1-10000−i3i300000000−i3−i3i3i30000i3−i300000000i3i3−i3−i30000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i3-222-20000000000001-1-110000
χ5122-2-2-2-222-12211-2-2-122-2-211-2-22222-2-2-1-1-1-121111-2-2-1-121111-1-1-2-222-1-10000-111-111-1-10000i3−i300000000i3i3−i3−i30000−i3i300000000−i3−i3i3i30000−i3i3i3−i3−i3−i3i3i3i3i3−i3−i3-222-20000000000001-1-110000
χ5222-2-2-2-222-12211-2-2-122-2-211-2-22222-2-2-1-1-1-121111-2-2-1-121111-1-1-2-222-1-10000-111-111-1-10000i3−i300000000i3i3−i3−i30000−i3i300000000−i3−i3i3i30000i3−i3−i3i3i3i3−i3−i3−i3−i3i3i32-2-22000000000000-111-10000
χ532-22-22i−2i2i−2i2222-22-2-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000022-2-22i−2i2i−2i000000000000000000000000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ542-22-22i−2i2i−2i2222-22-2-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i2222-22-22-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i000022-2-22i−2i2i−2i0000000000000000000000000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ552-22-2−2i2i−2i2i2222-22-2-2-2-22-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i2222-22-22-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i000022-2-2−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
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χ1264-4-444i−4i−4i4i-24-22-2-442-422-2−2i2i−2i2i2i−2i−4i4i4i−4i2i−2i-21-22-2-112-22-12−2i2ii−i−ii−2i2i2i−2i2i−2i00001-11-1i−i−ii00000000−2i32i30000i3−i3i3−i30000000023−230000−33−330000000000000000000000000000000000000000
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χ1294-4-444i−4i−4i4i-2-242-22-222-4-44−2i2i4i−4i−4i4i2i−2i−2i2i2i−2i1-2-2-112-22-2-122i−i−2i2i2i−2i−2i2i2i−2i−ii00001-11-1i−i−ii000000000000000000000000000000000000−2ζ5+2ζ132ζ5−2ζ132ζ7−2ζ23−2ζ7+2ζ230000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ1304-4-44−4i4i4i−4i4-2-2-442-2-4222-2−4i4i2i−2i−2i2i−2i2i2i−2i4i−4i-2-212-22-2-1122-12i−2i2i−2i−2i2i−iii−i−2i2i4-4−4i4i1-11-1−iii−i00-2200-220011-1-10000002i−2i002i−2i00−i−iii00000000000000000000000000000000000000000000
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χ1334-4-44−4i4i4i−4i-24-22-2-442-422-22i−2i2i−2i−2i2i4i−4i−4i4i−2i2i-21-22-2-112-22-122i−2i−iii−i2i−2i−2i2i−2i2i00001-11-1−iii−i00000000−2i32i30000i3−i3i3−i300000000−232300003−33−30000000000000000000000000000000000000000
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χ13788888888-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-4-42222222222222222222222220000-1-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000000000000000000000000
χ1388888-8-8-8-8-4-4-4-4-4-4-4-4-4-4-4-4444444444444222222222222-2-2-2-2-2-2-2-2-2-2-2-20000-1-1-1-111110000000000000000000000000000000000000000000000000000000000000000000000000000
χ13988-8-888-8-8-4-4-44444-4-4-444-4-4-4-44444-4-444222-2-2-2-2-2-22222222-2-222-2-2-2-20000-111-1-1-1110000000000000000000000000000000000000000000000000000000000000000000000000000
χ14088-8-8-8-888-4-4-44444-4-4-4444444-4-4-4-444-4-4222-2-2-2-2-2-2222-2-2-2-222-2-222220000-111-111-1-10000000000000000000000000000000000000000000000000000000000000000000000000000
χ1418-88-88i−8i8i−8i-4-4-4-44-44444-44−4i4i−4i4i−4i4i−4i4i−4i4i−4i4i2222-22-22-2-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i0000-1-111−ii−ii0000000000000000000000000000000000000000000000000000000000000000000000000000
χ1428-88-8−8i8i−8i8i-4-4-4-44-44444-444i−4i4i−4i4i−4i4i−4i4i−4i4i−4i2222-22-22-2-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i0000-1-111i−ii−i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ1438-8-888i−8i−8i8i-4-4-44-44-44444-4−4i4i−4i4i4i−4i4i−4i−4i4i4i−4i222-22-22-22-2-2-22i−2i2i−2i−2i2i2i−2i−2i2i−2i2i0000-11-11−iii−i0000000000000000000000000000000000000000000000000000000000000000000000000000
χ1448-8-88−8i8i8i−8i-4-4-44-44-44444-44i−4i4i−4i−4i4i−4i4i4i−4i−4i4i222-22-22-22-2-2-2−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i0000-11-11i−i−ii0000000000000000000000000000000000000000000000000000000000000000000000000000

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