Finite Group Databasebeta

← Group #13155521

Character table — Group #13155521

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size1111111122222222222222222222222244444444444444444444444466666666666666666666666688888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order122244443336666666661212121212121212121212123336666666661212121212121212121212122244444466661212121212121212121212123666121212126666668812121212121212121212121212121212121224242424242424242424242424242424444412121212121212128888242424242424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1111111-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
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
χ91111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111i−i11-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-1i−ii−iii−i−iii−i−ii−i
χ101111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1111111−ii11-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-1−ii−ii−i−iii−i−iii−ii
χ111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111i−i-1-111-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-11111i−i−iiii−i−i−i−iii−ii
χ121111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111−ii-1-111-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-11111−iii−i−i−iiiii−i−ii−i
χ131111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1i−i11-1-1111111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-11111−iii−i−i−iiiii−i−i−ii
χ141111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−ii11-1-1111111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-11111i−i−iiii−i−i−i−iiii−i
χ151111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1i−i-1-11111-1-1-1-111111111iiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-1−ii−ii−i−iii−i−iiii−i
χ161111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1−ii-1-11111-1-1-1-111111111−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-1i−ii−iii−i−iii−i−i−ii
χ172222222222-1222222-1-1-1-1-1-1-1222222222-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100222222-1-1-1-1-1-1-1-1-1-1-1-100000000000000002222-1-1-1-1-1-1-1-100000000000000
χ182222222222-1222222-1-1-1-1-1-1-1222222222-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-1222222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-22211111111-1-1-1-10000000000000000-2-2-2-21111111100000000000000
χ192222222222-1222222-1-1-1-1-1-1-1222222222-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-122-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111002222-2-2-1-1-1-1-1-1-1-111110000000000000000-2-2-2-21111111100000000000000
χ202222222222-1222222-1-1-1-1-1-1-1222222222-1-122-1-12-1-1-1-122-1-1-1-1-1-1-1-122-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-1-2-2111100-2-2-2-2-2-211111111111100000000000000002222-1-1-1-1-1-1-1-100000000000000
χ21222222222-12-1-1222-1222222222-1-122-1-1-12-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1220000-1-100000000-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000000000002200-1-1-1-1000000
χ22222222222-12-1-1222-1222222222-1-122-1-1-12-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20000-1-100000000-1-1-1-1-2-211-2-21111111111000000000000-2-2001111000000
χ23222222222-12-1-1222-1222222222-1-122-1-1-12-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-11111112200001100000000111122-1-122-1-1-1-1-1-1-1-1-1-1000000000000-2-2001111000000
χ24222222222-12-1-1222-1222222222-1-122-1-1-12-1-1-1-1-1-1222-1-1-12222-1-1-1-1-1-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1111111-2-2000011000000001111-2-211-2-211111111110000000000002200-1-1-1-1000000
χ2522222222-12222-1-1-122222222-1-122-1-122-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-1000022220000000022222222-1-1-1-1-1-1-1-100000022-1-1-1-100-1-1-1-1-1-1-1-10000-1-122-1-122-1-1-1-1-1-1-1-100000000000000220000-1-1-1-100
χ2622222222-12222-1-1-122222222-1-122-1-122-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-1000022220000000022222222-1-1-1-1-1-1-1-1000000-2-2-1-1-1-100-1-1-1-1-1-1-1-1000011-2-211-2-21111111100000000000000-2-20000111100
χ2722222222-12222-1-1-122222222-1-122-1-122-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-100000022111100111111110000-1-122-1-122-1-1-1-1-1-1-1-100000000000000-2-20000111100
χ2822222222-12222-1-1-122222222-1-122-1-122-1-12-1-122-1-1-1-12-1-1-1-1-1-12222-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1000000-2-211110011111111000011-2-211-2-21111111100000000000000220000-1-1-1-100
χ292222-2-2-2-222-1222222-1-1-11111-2-2-2-2-2-2-2-22-1-122-1-12-1-1-1-1-2-211111111-2-222-2-222-2-2-1-1-1-11111-1-1-1-11111-1-1-1-1111122-1-1-1-10022-2-2-2-2-1-1-1-111111111000000000000000022-2-2-1-1-1-1111100000000000000
χ302222-2-2-2-222-1222222-1-1-11111-2-2-2-2-2-2-2-22-1-122-1-12-1-1-1-1-2-211111111-2-222-2-2-2-222-1-1-1-111111111-1-1-1-1-1-1-1-1111122-1-1-1-100-2-222-2-21111-1-1-1-111110000000000000000-2-2221111-1-1-1-100000000000000
χ312222-2-2-2-222-1222222-1-1-11111-2-2-2-2-2-2-2-22-1-122-1-12-1-1-1-1-2-211111111-2-2-2-22222-2-21111-1-1-1-1-1-1-1-11111-1-1-1-11111-2-211110022-2-222-1-1-1-11111-1-1-1-10000000000000000-2-2221111-1-1-1-100000000000000
χ322222-2-2-2-222-1222222-1-1-11111-2-2-2-2-2-2-2-22-1-122-1-12-1-1-1-1-2-211111111-2-2-2-222-2-2221111-1-1-1-11111-1-1-1-1-1-1-1-11111-2-2111100-2-222221111-1-1-1-1-1-1-1-1000000000000000022-2-2-1-1-1-1111100000000000000
χ332222-2-2-2-22-12-1-1222-1222-2-2-2-2-2-211-2-211-12-1-1-1-1-1-1222-111-2-2-2-211111122-2-200002222-2-2-2-200000000-1-1-1-11111-1-1-1-1-1-12i−2i0000110000000011112i2i−i−i−2i−2iii−i−i−i−iiiii0000000000002i−2i00−i−iii000000
χ342222-2-2-2-22-12-1-1222-1222-2-2-2-2-2-211-2-211-12-1-1-1-1-1-1222-111-2-2-2-211111122-2-200002222-2-2-2-200000000-1-1-1-11111-1-1-1-1-1-1−2i2i000011000000001111−2i−2iii2i2i−i−iiiii−i−i−i−i000000000000−2i2i00ii−i−i000000
χ352222-2-2-2-22-12-1-1222-1222-2-2-2-2-2-211-2-211-12-1-1-1-1-1-1222-111-2-2-2-2111111-2-2220000-2-2-2-2222200000000-1-1-1-111111111112i−2i0000-1-100000000-1-1-1-12i2i−i−i−2i−2iii−i−i−i−iiiii000000000000−2i2i00ii−i−i000000
χ362222-2-2-2-22-12-1-1222-1222-2-2-2-2-2-211-2-211-12-1-1-1-1-1-1222-111-2-2-2-2111111-2-2220000-2-2-2-2222200000000-1-1-1-11111111111−2i2i0000-1-100000000-1-1-1-1−2i−2iii2i2i−i−iiiii−i−i−i−i0000000000002i−2i00−i−iii000000
χ372222-2-2-2-2-12222-1-1-12222-2-2-2-211-2-211-2-2-1-12-1-122-1-1-1-12111111-2-2-2-211000022-2-2000000002222-2-2-2-2-1-1-1-111110000002i−2i-1-11100-1-1-1-111110000−i−i2i2iii−2i−2i−i−i−i−iiiii000000000000002i−2i0000−i−iii00
χ382222-2-2-2-2-12222-1-1-12222-2-2-2-211-2-211-2-2-1-12-1-122-1-1-1-12111111-2-2-2-211000022-2-2000000002222-2-2-2-2-1-1-1-11111000000−2i2i-1-11100-1-1-1-111110000ii−2i−2i−i−i2i2iiiii−i−i−i−i00000000000000−2i2i0000ii−i−i00
χ392222-2-2-2-2-12222-1-1-12222-2-2-2-211-2-211-2-2-1-12-1-122-1-1-1-12111111-2-2-2-2110000-2-22200000000-2-2-2-22222-1-1-1-111110000002i−2i11-1-1001111-1-1-1-10000−i−i2i2iii−2i−2i−i−i−i−iiiii00000000000000−2i2i0000ii−i−i00
χ402222-2-2-2-2-12222-1-1-12222-2-2-2-211-2-211-2-2-1-12-1-122-1-1-1-12111111-2-2-2-2110000-2-22200000000-2-2-2-22222-1-1-1-11111000000−2i2i11-1-1001111-1-1-1-10000ii−2i−2i−i−i2i2iiiii−i−i−i−i000000000000002i−2i0000−i−iii00
χ4122-2-222-2-2222-2-22-2-222-2-222-2-2-2-2-2-22222222-2-2-2-222-2-222222-2-222-2-2-2-200002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i2-2-2222-2-2000000002i−2i2i−2i002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000000000
χ4222-2-222-2-2222-2-22-2-222-2-222-2-2-2-2-2-22222222-2-2-2-222-2-222222-2-222-2-2-2-20000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i2-2-2222-2-200000000−2i2i−2i2i00−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000000000
χ4322-2-222-2-222-1-2-22-2-22-111-1-111-2-2-2-222222-1-1-2-2112-111-122-1-111-1-111-2-200002i−2i2i−2i−i3−i3i3i3−i3−i3i3i3−i−iii−i−iii-111-1-1-11100−i3−i3i3i3002i−2i2i−2i00−i−iii−i−iii−i3−i3i3i30000000000000000000033−3−333−3−300000000000000
χ4422-2-222-2-222-1-2-22-2-22-111-1-111-2-2-2-222222-1-1-2-2112-111-122-1-111-1-111-2-200002i−2i2i−2ii3i3−i3−i3i3i3−i3−i3−i−iii−i−iii-111-1-1-11100i3i3−i3−i3002i−2i2i−2i00−i−iii−i−iiii3i3−i3−i300000000000000000000−3−333−3−33300000000000000
χ4522-2-222-2-222-1-2-22-2-22-111-1-111-2-2-2-222222-1-1-2-2112-111-122-1-111-1-111-2-20000−2i2i−2i2i−i3−i3i3i3−i3−i3i3i3ii−i−iii−i−i-111-1-1-11100−i3−i3i3i300−2i2i−2i2i00ii−i−iii−i−i−i3−i3i3i300000000000000000000−3−333−3−33300000000000000
χ4622-2-222-2-222-1-2-22-2-22-111-1-111-2-2-2-222222-1-1-2-2112-111-122-1-111-1-111-2-20000−2i2i−2i2ii3i3−i3−i3i3i3−i3−i3ii−i−iii−i−i-111-1-1-11100i3i3−i3−i300−2i2i−2i2i00ii−i−iii−i−ii3i3−i3−i30000000000000000000033−3−333−3−300000000000000
χ4722-2-222-2-2-122-2-2-11122-2-222-2-211-2-2-1-122-1-1211-2-2-1-1112-1-1-1-11122-2-21100002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i-111-1-1-11100000000−ii−ii00−i−iii−i−iii00003−3003−30033−3−333−3−300000000000000000000−i3i3−i3i300
χ4822-2-222-2-2-122-2-2-11122-2-222-2-211-2-2-1-122-1-1211-2-2-1-1112-1-1-1-11122-2-21100002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i-111-1-1-11100000000−ii−ii00−i−iii−i−iii0000−3300−3300−3−333−3−33300000000000000000000i3−i3i3−i300
χ4922-2-222-2-2-122-2-2-11122-2-222-2-211-2-2-1-122-1-1211-2-2-1-1112-1-1-1-11122-2-2110000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i-111-1-1-11100000000i−ii−i00ii−i−iii−i−i00003−3003−30033−3−333−3−300000000000000000000i3−i3i3−i300
χ5022-2-222-2-2-122-2-2-11122-2-222-2-211-2-2-1-122-1-1211-2-2-1-1112-1-1-1-11122-2-2110000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i-111-1-1-11100000000i−ii−i00ii−i−iii−i−i0000−3300−3300−3−333−3−33300000000000000000000−i3i3−i3i300
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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
χ15188-8-888-8-8-4-4-444-444-4-444-4-4444444-4-4-4-4222-2-2-2-222-2-222222-2-222-2-2-2-2000000000000000000000000-111-1-1-11100000000000000000000000000000000000000000000000000000000000000000000
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χ1558-8-888i−8i−8i8i-4-4-44-444-4444-4−4i4i4i−4i4i−4i4i−4i−4i4i−4i4i222-22-22-2-2-22-22i−2i2i−2i−2i2i2i−2i−2i2i−2i2i000000000000000000000000-11-11−iii−i00000000000000000000000000000000000000000000000000000000000000000000
χ1568-8-88−8i8i8i−8i-4-4-44-444-4444-44i−4i−4i4i−4i4i−4i4i4i−4i4i−4i222-22-22-2-2-22-2−2i2i−2i2i2i−2i−2i2i2i−2i2i−2i000000000000000000000000-11-11i−i−ii00000000000000000000000000000000000000000000000000000000000000000000

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