Finite Group Databasebeta

← Group #13155753

Character table — Group #13155753

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order12442333466666121212121212121233366666666612121212121212121212121288882424242436666121212121288882424242424242424242424242424242424242424242424242424242424242424242424242424242424446688121212121212242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-111-1-111
χ81111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ911-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1111-1-1-1-1ii−i−iii−i−i1-1-1-11111-1-1i−i1-1ii−i−i11-1-1i−iii−i−iiiii−i−i−i−i111111-1-1-1-1-1-1i−iii−i−i1-1i−i11i−iii−i−i-1-1i−i1-1
χ1011-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1111-1-1-1-1ii−i−iii−i−i1-1-1-11111-1-1i−i-11ii−i−i-1-111i−iii−i−iiiii−i−i−i−i-1-1-1-1-1-1111111i−iii−i−i1-1−ii11−ii−i−iii-1-1−ii-11
χ1111-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1111-1-1-1-1ii−i−iii−i−i1-1-1-11111-1-1−ii1-1ii−i−i11-1-1i−i−i−iiiiiii−i−i−i−i111111-1-1-1-1-1-1−ii−i−iii-11i−i-1-1−iiii−i−i11−ii-11
χ1211-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1111-1-1-1-1ii−i−iii−i−i1-1-1-11111-1-1−ii-11ii−i−i-1-111i−i−i−iiiiiii−i−i−i−i-1-1-1-1-1-1111111−ii−i−iii-11−ii-1-1i−i−i−iii11i−i1-1
χ1311-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1111-1-1-1-1−i−iii−i−iii1-1-1-11111-1-1i−i1-1−i−iii11-1-1−iiii−i−i−i−i−i−iiiii111111-1-1-1-1-1-1i−iii−i−i-11−ii-1-1i−i−i−iii11i−i-11
χ1411-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1111-1-1-1-1−i−iii−i−iii1-1-1-11111-1-1i−i-11−i−iii-1-111−iiii−i−i−i−i−i−iiiii-1-1-1-1-1-1111111i−iii−i−i-11i−i-1-1−iiii−i−i11−ii1-1
χ1511-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1111-1-1-1-1−i−iii−i−iii1-1-1-11111-1-1−ii1-1−i−iii11-1-1−ii−i−iii−i−i−i−iiiii111111-1-1-1-1-1-1−ii−i−iii1-1−ii11−ii−i−iii-1-1−ii1-1
χ1611-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-1111-1-1-1-1−i−iii−i−iii1-1-1-11111-1-1−ii-11−i−iii-1-111−ii−i−iii−i−i−i−iiiii-1-1-1-1-1-1111111−ii−i−iii1-1i−i11i−iii−i−i-1-1i−i-11
χ172222222-122222-12222-1-1222-1-12-122-1-12-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1220022220000-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-12200-1-1000000-1-10000
χ182222222-122222-12222-1-1222-1-12-122-1-12-1-1-1-1-122222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20022220000-1-11111-1-1-1-1-1-1-1-1000000000000-2-21111-2-20011000000110000
χ192222222-122222-12222-1-1222-1-12-122-1-12-1-1-1-1-122222-1-1-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-12200-2-2-2-2000011-1-1-1-11111111100000000000022-1-1-1-1-2-20011000000110000
χ202222222-122222-12222-1-1222-1-12-122-1-12-1-1-1-1-122222-1-1-1-1-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2000011111111111111000000000000-2-211112200-1-1000000-1-10000
χ21222222-1222-1222222222-1-1-12-1-12-1-122-12-1222-1-1-1-1-122-1-100000000-1-1-1-1-1-1-1-1-1-122220000222200222200000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000022000000-1-100
χ22222222-1222-1222222222-1-1-12-1-12-1-122-12-1222-1-1-1-1-122-1-100000000-1-1-1-1-1-1-1-1-1-122-2-20000-2-2-2-200222200000000111111111111-1-1-1-1-1-1000000-2-20000001100
χ23222222-1222-1222222222-1-1-12-1-12-1-122-12-1222-1-1-1-1-122-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2220000222200-2-2-2-200000000-1-1-1-1-1-1-1-1-1-1-1-1111111000000-2-20000001100
χ24222222-1222-1222222222-1-1-12-1-12-1-122-12-1222-1-1-1-1-122-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-200-2-2-2-20000000011111111111111111100000022000000-1-100
χ2522222-1222-12-1-12-1-1-1-12222-1-1222-1-1-1-1-1-122-1-1-1-12-1-1-1-12222222222-12-1-1-12-1-1-1-10022-1-1-1-1-1-1-1-1220000-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100000000220000-1-1-1-1000000
χ2622222-1222-12-1-12-1-1-1-12222-1-1222-1-1-1-1-1-122-1-1-1-12-1-1-1-12222222222-12-1-1-12-1-1-1-100-2-2-1-1-1-11111220000-1-1-1-1-1-1-1-1-2-21111-2-2111100000000-2-200001111000000
χ2722222-1222-12-1-12-1-1-1-12222-1-1222-1-1-1-1-1-122-1-1-1-12-1-1-1-122-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-100221111-1-1-1-1-2-200001111111122-1-1-1-122-1-1-1-100000000-2-200001111000000
χ2822222-1222-12-1-12-1-1-1-12222-1-1222-1-1-1-1-1-122-1-1-1-12-1-1-1-122-2-2-2-2-2-2-2-2-12-1-1-12-1-1-1-100-2-211111111-2-2000011111111-2-21111-2-2111100000000220000-1-1-1-1000000
χ292222-2222-222-2-22-2-2222222222-2-2-2-2-2-2222-2-2-222-2-2-222222-22-222222-2-2-22-2-2-22200002-22-20000-2-2000022-2-222-2-2000000000000000000000000000000000000
χ302222-2222-222-2-22-2-2222222222-2-2-2-2-2-2222-2-2-222-2-2-22222-22-22-2-2-2-22-2-2-22-2-2-2220000-22-220000220000-2-222-2-222000000000000000000000000000000000000
χ312222-222-1-222-2-2-1-2-222-1-1222-1-1-21-2-2112-1-111122-2-2-2-1-1-1-12-22-2-1-1-1-1-1111-1111-1-100002-22-2000011−i3i3−i3i3-1-111-1-11100000000000000−i3i3−i3i30000−i3i3000000−i3i30000
χ322222-222-1-222-2-2-1-2-222-1-1222-1-1-21-2-2112-1-111122-2-2-2-1-1-1-12-22-2-1-1-1-1-1111-1111-1-100002-22-2000011i3−i3i3−i3-1-111-1-11100000000000000i3−i3i3−i30000i3−i3000000i3−i30000
χ332222-222-1-222-2-2-1-2-222-1-1222-1-1-21-2-2112-1-111122-2-2-2-1-1-1-1-22-221111-1111-1111-1-10000-22-220000-1-1−i3i3−i3i311-1-111-1-100000000000000−i3i3−i3i30000i3−i3000000i3−i30000
χ342222-222-1-222-2-2-1-2-222-1-1222-1-1-21-2-2112-1-111122-2-2-2-1-1-1-1-22-221111-1111-1111-1-10000-22-220000-1-1i3−i3i3−i311-1-111-1-100000000000000i3−i3i3−i30000−i3i3000000−i3i30000
χ352222-2-122-2-1211211-1-12222-1-12-2-21111-1-12-211-1-1-211-1-1222-22-22222-1-211-1-211-1-10000-11-113−33−3-2-20000-1-111-1-1110033−3−30033−3−3000000000000003−33−3000000
χ362222-2-122-2-1211211-1-12222-1-12-2-21111-1-12-211-1-1-211-1-1222-22-22222-1-211-1-211-1-10000-11-11−33−33-2-20000-1-111-1-11100−3−33300−3−33300000000000000−33−33000000
χ372222-2-122-2-1211211-1-12222-1-12-2-21111-1-12-211-1-1-211-1-122-22-22-2-2-2-2-1-211-1-211-1-100001-11-13−33−322000011-1-111-1-10033−3−30033−3−300000000000000−33−33000000
χ382222-2-122-2-1211211-1-12222-1-12-2-21111-1-12-211-1-1-211-1-122-22-22-2-2-2-2-1-211-1-211-1-100001-11-1−33−3322000011-1-111-1-100−3−33300−3−333000000000000003−33−3000000
χ3922-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22i−2i−2i2i2i2i−2i−2i22222-2-2-2-2-200002i−2i−2i2i0000−2i2i00002i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000
χ4022-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2−2i2i2i−2i−2i−2i2i2i22222-2-2-2-2-20000−2i2i2i−2i00002i−2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000
χ4122-2-2222-1-22222-1-2-2-2-211-2-22-1-12-122-1-12-1-1111-2-2-2-2-211112i−2i−2i2i−i−iii-1-1-1-1-11111100002i−2i−2i2i0000i−i3−3−33−i−iiiii−i−i000000000000003−3−330000−i3i3000000i3−i30000
χ4222-2-2222-1-22222-1-2-2-2-211-2-22-1-12-122-1-12-1-1111-2-2-2-2-211112i−2i−2i2i−i−iii-1-1-1-1-11111100002i−2i−2i2i0000i−i−333−3−i−iiiii−i−i00000000000000−333−30000i3−i3000000−i3i30000
χ4322-2-2222-1-22222-1-2-2-2-211-2-22-1-12-122-1-12-1-1111-2-2-2-2-21111−2i2i2i−2iii−i−i-1-1-1-1-1111110000−2i2i2i−2i0000−ii3−3−33ii−i−i−i−iii000000000000003−3−330000i3−i3000000−i3i30000
χ4422-2-2222-1-22222-1-2-2-2-211-2-22-1-12-122-1-12-1-1111-2-2-2-2-21111−2i2i2i−2iii−i−i-1-1-1-1-1111110000−2i2i2i−2i0000−ii−333−3ii−i−i−i−iii00000000000000−333−30000−i3i3000000i3−i30000
χ4522-2-22-122-2-12-1-121111-2-2-2-2-1-1222-1-1-1-1-1-12-21111-21111-2-22i−2i−2i2i2i2i−2i−2i-12-1-1-1-211110000−iii−i3−3−33−2i2i0000−i−iiiii−i−i0033−3−300−3−33300000000000000i3−i3−i3i3000000
χ4622-2-22-122-2-12-1-121111-2-2-2-2-1-1222-1-1-1-1-1-12-21111-21111-2-22i−2i−2i2i2i2i−2i−2i-12-1-1-1-211110000−iii−i−333−3−2i2i0000−i−iiiii−i−i00−3−3330033−3−300000000000000−i3i3i3−i3000000
χ4722-2-22-122-2-12-1-121111-2-2-2-2-1-1222-1-1-1-1-1-12-21111-21111-2-2−2i2i2i−2i−2i−2i2i2i-12-1-1-1-211110000i−i−ii3−3−332i−2i0000ii−i−i−i−iii0033−3−300−3−33300000000000000−i3i3i3−i3000000
χ4822-2-22-122-2-12-1-121111-2-2-2-2-1-1222-1-1-1-1-1-12-21111-21111-2-2−2i2i2i−2i−2i−2i2i2i-12-1-1-1-211110000i−i−ii−333−32i−2i0000ii−i−i−i−iii00−3−3330033−3−300000000000000i3−i3−i3i3000000
χ4922-2-2-222-1222-2-2-122-2-211-2-22-1-1-21-2-2112-1-1-1-1-1-2-222211112i2i−2i−2i−i−iii-1111-1-1-1-1112i−2i002i2i−2i−2i0000−ii−i−iii−i−i−i−iiiii0000000000002i−2i−i−iii2-200-1-1000000110000
χ5022-2-2-222-1222-2-2-122-2-211-2-22-1-1-21-2-2112-1-1-1-1-1-2-222211112i2i−2i−2i−i−iii-1111-1-1-1-111−2i2i002i2i−2i−2i0000−iiii−i−i−i−i−i−iiiii000000000000−2i2iii−i−i-220011000000-1-10000
χ5122-2-2-222-1222-2-2-122-2-211-2-22-1-1-21-2-2112-1-1-1-1-1-2-22221111−2i−2i2i2iii−i−i-1111-1-1-1-1112i−2i00−2i−2i2i2i0000i−i−i−iiiiiii−i−i−i−i0000000000002i−2i−i−iii-220011000000-1-10000
χ5222-2-2-222-1222-2-2-122-2-211-2-22-1-1-21-2-2112-1-1-1-1-1-2-22221111−2i−2i2i2iii−i−i-1111-1-1-1-111−2i2i00−2i−2i2i2i0000i−iii−i−iiiii−i−i−i−i000000000000−2i2iii−i−i2-200-1-1000000110000
χ5322-2-2-22-1222-1-2-2222-2-2-2-211-12-11-211-2-2-12-122211-1-1-1-2-21100000000-1111-1-1-1-1112i−2i2-2000022-2-2002i2i−2i−2i00000000-1-1-1-1-1-1111111−ii−i−iii0000002i−2i000000−ii00
χ5422-2-2-22-1222-1-2-2222-2-2-2-211-12-11-211-2-2-12-122211-1-1-1-2-21100000000-1111-1-1-1-1112i−2i-220000-2-222002i2i−2i−2i00000000111111-1-1-1-1-1-1−ii−i−iii000000−2i2i000000i−i00
χ5522-2-2-22-1222-1-2-2222-2-2-2-211-12-11-211-2-2-12-122211-1-1-1-2-21100000000-1111-1-1-1-111−2i2i2-2000022-2-200−2i−2i2i2i00000000-1-1-1-1-1-1111111i−iii−i−i000000−2i2i000000i−i00
χ5622-2-2-22-1222-1-2-2222-2-2-2-211-12-11-211-2-2-12-122211-1-1-1-2-21100000000-1111-1-1-1-111−2i2i-220000-2-22200−2i−2i2i2i00000000111111-1-1-1-1-1-1i−iii−i−i0000002i−2i000000−ii00
χ5722-2-2-2-1222-12112-1-111-2-2-2-2-1-12-2-21111-1-122-1-1112-1-111-2-22i2i−2i−2i2i2i−2i−2i-1-211-12-1-111002-2−i−iii-1-1112i−2i0000−i−i−i−iiiii22-1-1-1-1-2-21111000000002i−2i0000−i−iii000000
χ5822-2-2-2-1222-12112-1-111-2-2-2-2-1-12-2-21111-1-122-1-1112-1-111-2-22i2i−2i−2i2i2i−2i−2i-1-211-12-1-11100-22−i−iii11-1-12i−2i0000−i−i−i−iiiii-2-2111122-1-1-1-100000000−2i2i0000ii−i−i000000
χ5922-2-2-2-1222-12112-1-111-2-2-2-2-1-12-2-21111-1-122-1-1112-1-111-2-2−2i−2i2i2i−2i−2i2i2i-1-211-12-1-111002-2ii−i−i-1-111−2i2i0000iiii−i−i−i−i22-1-1-1-1-2-2111100000000−2i2i0000ii−i−i000000
χ6022-2-2-2-1222-12112-1-111-2-2-2-2-1-12-2-21111-1-122-1-1112-1-111-2-2−2i−2i2i2i−2i−2i2i2i-1-211-12-1-11100-22ii−i−i11-1-1−2i2i0000iiii−i−i−i−i-2-2111122-1-1-1-1000000002i−2i0000−i−iii000000
χ61444444-2-244-244-24444-2-2-2-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-21100000000111111111144000000000000-2-2-2-200000000000000000000-2-21111000000000000000000
χ62444444-2-244-244-24444-2-2-2-2-2-21-2-2-2-2-2-2-2-21-2-2-2-2-2-2-2-2-2-211000000001111111111-4-400000000000022220000000000000000000022-1-1-1-1000000000000000000
χ6344444-24-24-24-2-2-2-2-2-2-2-2-244-21-24-2-2-211-21-2-211-2-24-2-211-2-24444-2-2-2-21-2111-211110000-2-2-2-20000-2-2000011111111000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.