Finite Group Databasebeta

← Group #13156789

Character table — Group #13156789

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156
size1111111122222222222222222222222244444444444444444444444466666666666666666666666688888888121212121212121212121212121212121212121212121212121212121212121212121212121212121212181818181818181818181818363636363636363636363636108108
order122222223336666666666666666666663336666666666666666666664444444412121212121212121212121212121212366666664412121212121212121212121212121212121212121212121212121212121212121212121212121212444412121212121212124444121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
χ511111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1
χ611111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111
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
χ911-1-1-111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1i−iii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-11111-1-1-1-11-11-111-1-111-1-1i−i
χ1011-1-1-111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1111-1-1-1-1−iiii−i−iii−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii11-1-11111-1-1-1-1-11-11-1-111-1-111−ii
χ1111-1-1-111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1i−iii−i−i−i−iiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-11111-111-111-1-1-1-111−ii
χ1211-1-1-111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1−iiii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1-1-111111-1-11-1-11111-1-1i−i
χ1311-1-1-111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1i−i−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i-1-111-1-1-1-111111-1-11-1-11111-1-1−ii
χ1411-1-1-111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1−ii−i−iiiii−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-11111-111-111-1-1-1-111i−i
χ1511-1-1-111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1i−i−i−iii−i−iiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i11-1-11111-1-1-1-1-11-11-1-111-1-111i−i
χ1611-1-1-111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1111-1-1-1-1−ii−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii11-1-11111-1-1-1-11-11-111-1-111-1-1−ii
χ172222222222-12222-1-12222-1-12222-1-122-12-1-1222-1-1-1-1-1-1222-1-1-1-1-1-12-1-1000022220000000022222222-1-1-1-1-1-1-1-1220000-1-1-1-122-1-122-1-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022000000-1-1-1-100
χ182222222222-12222-1-12222-1-12222-1-122-12-1-1222-1-1-1-1-1-1222-1-1-1-1-1-12-1-1000022220000000022222222-1-1-1-1-1-1-1-1-2-20000-1-1-1-1-2-211-2-21100000000-1-1-1-1-1-1-1-111111111000000000000-2-2000000111100
χ192222222222-12222-1-12222-1-12222-1-122-12-1-1222-1-1-1-1-1-1222-1-1-1-1-1-12-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1220000111122-1-122-1-10000000011111111-1-1-1-1-1-1-1-1000000000000-2-2000000111100
χ202222222222-12222-1-12222-1-12222-1-122-12-1-1222-1-1-1-1-1-1222-1-1-1-1-1-12-1-10000-2-2-2-200000000-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-2-200001111-2-211-2-21100000000111111111111111100000000000022000000-1-1-1-100
χ21222222222-1222-1-12222-1-12222-1-1222-12-12-1-1-1-1222-1-1-1-1-1-1222-1-1-1-12-1222200002222222200000000-1-1-1-1-1-1-1-122-1-1-1-10000-1-122-1-122-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-10000000000000022-1-1-1-1000000
χ22222222222-1222-1-12222-1-12222-1-1222-12-12-1-1-1-1222-1-1-1-1-1-1222-1-1-1-12-1222200002222222200000000-1-1-1-1-1-1-1-1-2-2-1-1-1-1000011-2-211-2-2-1-1-1-1-1-1-1-1000000001111111100000000000000-2-21111000000
χ23222222222-1222-1-12222-1-12222-1-1222-12-12-1-1-1-1222-1-1-1-1-1-1222-1-1-1-12-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-12211110000-1-122-1-1221111111100000000-1-1-1-1-1-1-1-100000000000000-2-21111000000
χ24222222222-1222-1-12222-1-12222-1-1222-12-12-1-1-1-1222-1-1-1-1-1-1222-1-1-1-12-1-2-2-2-20000-2-2-2-2-2-2-2-200000000-1-1-1-1-1-1-1-1-2-21111000011-2-211-2-21111111100000000111111110000000000000022-1-1-1-1000000
χ2522222222-122-1-12222-1-12222-1-12222-122-1-12-1-1-1-1-1-1222-1-1-1-1-1-1222-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002222222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000002222-1-1-1-1-1-1-1-100000000000000
χ2622222222-122-1-12222-1-12222-1-12222-122-1-12-1-1-1-1-1-1222-1-1-1-1-1-1222-1-122222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1002222-2-2-2-200000000-1-1-1-1-1-1-1-11111111100000000-2-2-2-21111111100000000000000
χ2722222222-122-1-12222-1-12222-1-12222-122-1-12-1-1-1-1-1-1222-1-1-1-1-1-1222-1-12-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-222220000000011111111-1-1-1-1-1-1-1-100000000-2-2-2-21111111100000000000000
χ2822222222-122-1-12222-1-12222-1-12222-122-1-12-1-1-1-1-1-1222-1-1-1-1-1-1222-1-12-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-100-2-2-2-2-2-2-2-2000000001111111111111111000000002222-1-1-1-1-1-1-1-100000000000000
χ292222-2-2-2-22222-22-22-22-22-2222-22-2-2-2-2-2-22222-2-22-2-22-2-22-2-222-222-22-2-22-22-2000022-2-222-2-20000000022-2-222-2-2002-22-200000000000022-2-222-2-2000000000000000000000000000000000000000000
χ302222-2-2-2-22222-22-22-22-22-2222-22-2-2-2-2-2-22222-2-22-2-22-2-22-2-222-222-22-2-2-22-220000-2-222-2-2220000000022-2-222-2-200-22-22000000000000-2-222-2-222000000000000000000000000000000000000000000
χ312222-2-2-2-22-122-2-112-22-2-11222-2-11-2-2-21-2-12-1-1112-2-2-111-11122-2-1-11-1-212-22-2000022-2-222-2-200000000-1-111-1-11100-11-1100003−3003−300-1-111-1-1110000000033−3−333−3−300000000000000003−33−3000000
χ322222-2-2-2-22-122-2-112-22-2-11222-2-11-2-2-21-2-12-1-1112-2-2-111-11122-2-1-11-1-212-22-2000022-2-222-2-200000000-1-111-1-11100-11-110000−3300−3300-1-111-1-11100000000−3−333−3−3330000000000000000−33−33000000
χ332222-2-2-2-22-122-2-112-22-2-11222-2-11-2-2-21-2-12-1-1112-2-2-111-11122-2-1-11-1-21-22-220000-2-222-2-22200000000-1-111-1-111001-11-100003−3003−30011-1-111-1-10000000033−3−333−3−30000000000000000−33−33000000
χ342222-2-2-2-22-122-2-112-22-2-11222-2-11-2-2-21-2-12-1-1112-2-2-111-11122-2-1-11-1-21-22-220000-2-222-2-22200000000-1-111-1-111001-11-10000−3300−330011-1-111-1-100000000−3−333−3−33300000000000000003−33−3000000
χ352222-2-2-2-2-122-112-22-2-112-222-112-2-2-21-2-2-1-12-111-1112-2-2-111-1-1122-2-11-22-22-20000-1-111-1-11133−3−333−3−3-1-111-1-111002-22-2000000000000-1-111-1-11133−3−333−3−300000000000033−3−333−3−300000000000000
χ362222-2-2-2-2-122-112-22-2-112-222-112-2-2-21-2-2-1-12-111-1112-2-2-111-1-1122-2-11-22-22-20000-1-111-1-111−3−333−3−333-1-111-1-111002-22-2000000000000-1-111-1-111−3−333−3−333000000000000−3−333−3−33300000000000000
χ372222-2-2-2-2-122-112-22-2-112-222-112-2-2-21-2-2-1-12-111-1112-2-2-111-1-1122-2-11-2-22-22000011-1-111-1-133−3−333−3−3-1-111-1-11100-22-2200000000000011-1-111-1-133−3−333−3−3000000000000−3−333−3−33300000000000000
χ382222-2-2-2-2-122-112-22-2-112-222-112-2-2-21-2-2-1-12-111-1112-2-2-111-1-1122-2-11-2-22-22000011-1-111-1-1−3−333−3−333-1-111-1-11100-22-2200000000000011-1-111-1-1−3−333−3−33300000000000033−3−333−3−300000000000000
χ3922-2-22-2-222222-22-22-2-22-22-2-2-22-2222-2-2-22222-2-22-2-22-2-2-222-2-22-2-22-2222i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i0000000022-2-2-2-222002i−2i−2i2i0000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000
χ4022-2-22-2-222222-22-22-2-22-22-2-2-22-2222-2-2-22222-2-22-2-22-2-2-222-2-22-2-22-222−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i0000000022-2-2-2-22200−2i2i2i−2i000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000
χ4122-2-22-2-222-122-2-112-2-221-1-2-2-221-122-21-2-12-1-1112-2-2-1111-1-1-2-2211-112-12i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000-1-11111-1-100−iii−i0000−i3i300i3−i300−i−iiiii−i−i00000000−i3−i3i3i3i3i3−i3−i30000000000000000−333−3000000
χ4222-2-22-2-222-122-2-112-2-221-1-2-2-221-122-21-2-12-1-1112-2-2-1111-1-1-2-2211-112-12i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000-1-11111-1-100−iii−i0000i3−i300−i3i300−i−iiiii−i−i00000000i3i3−i3−i3−i3−i3i3i300000000000000003−3−33000000
χ4322-2-22-2-222-122-2-112-2-221-1-2-2-221-122-21-2-12-1-1112-2-2-1111-1-1-2-2211-112-1−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000-1-11111-1-100i−i−ii0000−i3i300i3−i300ii−i−i−i−iii00000000−i3−i3i3i3i3i3−i3−i300000000000000003−3−33000000
χ4422-2-22-2-222-122-2-112-2-221-1-2-2-221-122-21-2-12-1-1112-2-2-1111-1-1-2-2211-112-1−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000-1-11111-1-100i−i−ii0000i3−i300−i3i300ii−i−i−i−iii00000000i3i3−i3−i3−i3−i3i3i30000000000000000−333−3000000
χ4522-2-22-2-22-122-112-22-21-1-22-2-21-1-22221-2-2-1-12-111-1112-2-21-1-111-1-2-221-122i−2i−2i2i0000−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3-1-11111-1-1002i−2i−2i2i000000000000−i−iiiii−i−i−i3−i3i3i3i3i3−i3−i3000000000000−3−33333−3−300000000000000
χ4622-2-22-2-22-122-112-22-21-1-22-2-21-1-22221-2-2-1-12-111-1112-2-21-1-111-1-2-221-122i−2i−2i2i0000−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i3-1-11111-1-1002i−2i−2i2i000000000000−i−iiiii−i−ii3i3−i3−i3−i3−i3i3i300000000000033−3−3−3−33300000000000000
χ4722-2-22-2-22-122-112-22-21-1-22-2-21-1-22221-2-2-1-12-111-1112-2-21-1-111-1-2-221-12−2i2i2i−2i0000ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i3-1-11111-1-100−2i2i2i−2i000000000000ii−i−i−i−iii−i3−i3i3i3i3i3−i3−i300000000000033−3−3−3−33300000000000000
χ4822-2-22-2-22-122-112-22-21-1-22-2-21-1-22221-2-2-1-12-111-1112-2-21-1-111-1-2-221-12−2i2i2i−2i0000ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3-1-11111-1-100−2i2i2i−2i000000000000ii−i−i−i−iiii3i3−i3−i3−i3−i3i3i3000000000000−3−33333−3−300000000000000
χ4922-2-2-222-222-12222-1-1-2-2-2-211-2-2-2-21122-12-1-1222-1-1-1-1-1-1-2-2-2111111-21100002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-1-1-1-111112i−2i0000−i−iii2i2i−i−i−2i−2iii00000000−i−i−i−iiiii−i−i−i−iiiii0000000000002-2000000-1-11100
χ5022-2-2-222-222-12222-1-1-2-2-2-211-2-2-2-21122-12-1-1222-1-1-1-1-1-1-2-2-2111111-21100002i2i−2i−2i000000002i2i2i2i−2i−2i−2i−2i-1-1-1-11111−2i2i0000−i−iii−2i−2iii2i2i−i−i00000000−i−i−i−iiiiiiiii−i−i−i−i000000000000-2200000011-1-100
χ5122-2-2-222-222-12222-1-1-2-2-2-211-2-2-2-21122-12-1-1222-1-1-1-1-1-1-2-2-2111111-2110000−2i−2i2i2i00000000−2i−2i−2i−2i2i2i2i2i-1-1-1-111112i−2i0000ii−i−i2i2i−i−i−2i−2iii00000000iiii−i−i−i−i−i−i−i−iiiii000000000000-2200000011-1-100
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χ1244-44-44-44-4-2-242222-44-2-2-224-4222-24-4-2-2-41-2-2-11-12-222-2211-1-22-2-222-12-20000000023−2323−2323−2323−23000000001-11-11-11-1000000000000000000−33−33−33−33000000000000000000000000000000000000000000
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χ1264-44-4-44-4444-2-44-44224-444-22-44-4-42-2-4-4-24-2-2-4-4422-222-24-44-222-22-2-4-22000000000000000000000000-222-2-222-200000000000000000000000000000000000000000000000000000000000000000000
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χ1284-44-4-44-444-2-2-442-2224-4-2-2-22-44222-2-42-2-2-2122-222-2-1-11-22-2-2221-112-2-10000000000000000000000001-1-111-1-1100000000000000000000000000000000003i−3i−3i3i3i−3i−3i3i00000000000000000000000000
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χ1384-4-4444-4-4-24-22-2-44222-2-4-42-2-2244-222-4-2-21-222-2-1-1122-22-22-1112-22-2-1-2000000000000000023−23−2323−232323−231-1-11-111-100000000000000000000000000−333−33−3−330000000000000000000000000000000000
χ1394-4-4444-4-4-24-22-2-44222-2-4-42-2-2244-222-4-2-21-222-2-1-1122-22-22-1112-22-2-1-20000000000000000−232323−2323−23−23231-1-11-111-1000000000000000000000000003−3−33−333−30000000000000000000000000000000000
χ1404-4-4444-4-4-2-242-22-2-4-42-222-44-22-2-24-42241-2-2-1-1122-222-2-11-12-2-22-2212-200000000−2i32i32i3−2i32i3−2i3−2i32i3000000001-1-11-111-1000000000000000000i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000000000000000
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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
χ1508888-8-8-8-8-4-4-4-44-44-44-44-44-4-4-44-44444442222-2-22-2-22-2-22-2-222-222-22-2-2000000000000000000000000-1-111-1-11100000000000000000000000000000000000000000000000000000000000000000000
χ15188-8-88-8-88-4-4-4-44-44-444-44-4444-44-4-4-44442222-2-22-2-22-2-2-222-2-22-2-22-222000000000000000000000000-1-11111-1-100000000000000000000000000000000000000000000000000000000000000000000
χ15288-8-8-888-8-4-4-4-4-4-4-4-4-4444444444444-4-4-4222222222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000-1-1-1-1111100000000000000000000000000000000000000000000000000000000000000000000
χ1538-88-88-88-8-4-4-444444-4-4-4-44-44444-4-44-4-44222-22-2-22-2-22-222-22-222-2-2-2-22000000000000000000000000-11-11-11-1100000000000000000000000000000000000000000000000000000000000000000000
χ1548-88-8-88-88-4-4-44-44-444-44-4-4-444-4444-444-4222-2-22-2-22-2-222-222-2-22-22-22-2000000000000000000000000-111-1-111-100000000000000000000000000000000000000000000000000000000000000000000
χ1558-8-8888-8-8-4-4-44-44-4444-4444-4-44-4-4-4444-4222-2-22-2-22-2-22-22-2-222-22-22-22000000000000000000000000-111-11-1-1100000000000000000000000000000000000000000000000000000000000000000000
χ1568-8-88-8-888-4-4-444444-4444-44-4-4-4-444-4-4-44222-22-2-22-2-22-2-2-22-22-2-22222-2000000000000000000000000-11-111-11-100000000000000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).