Finite Group Databasebeta

← Group #13155757

Character table — Group #13155757

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181818182424242424242424363636363636363672727272108108
order124423334666661212121212121212333666666666121212121212121212121212366661212121212448888121212121212121212121212121212122424242424242424242424242424242488882424242424242424248824242424612242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ511111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1
χ911-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-11-1-1-11111-1-1i−ii−i1-1ii−i−iiiiiii−i−i−i−i−i−i11-1-1111111-1-1-1-1-1-1ii−i−ii−ii−iii−i−i1-1i−iii−i−i1-1i−i1-1
χ1011-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-11-1-1-11111-1-1i−ii−i-11ii−i−iiiiiii−i−i−i−i−i−i-1-111-1-1-1-1-1-1111111−i−iiii−ii−iii−i−i1-1−ii−i−iii1-1−ii-11
χ1111-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-11-1-1-11111-1-1i−i−ii1-1ii−i−iiiiiii−i−i−i−i−i−i11-1-1111111-1-1-1-1-1-1ii−i−i−ii−ii−i−iii-11−iiii−i−i-11−ii-11
χ1211-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-11-1-1-11111-1-1i−i−ii-11ii−i−iiiiiii−i−i−i−i−i−i-1-111-1-1-1-1-1-1111111−i−iii−ii−ii−i−iii-11i−i−i−iii-11i−i1-1
χ1311-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-11-1-1-11111-1-1−iii−i1-1−i−iii−i−i−i−i−i−iiiiiii11-1-1111111-1-1-1-1-1-1−i−iiii−ii−iii−i−i-11i−i−i−iii-11i−i-11
χ1411-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-11-1-1-11111-1-1−iii−i-11−i−iii−i−i−i−i−i−iiiiiii-1-111-1-1-1-1-1-1111111ii−i−ii−ii−iii−i−i-11−iiii−i−i-11−ii1-1
χ1511-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-11-1-1-11111-1-1−ii−ii1-1−i−iii−i−i−i−i−i−iiiiiii11-1-1111111-1-1-1-1-1-1−i−iii−ii−ii−i−iii1-1−ii−i−iii1-1−ii1-1
χ1611-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1111-1-1-1111-1-1-1-1111-1-11-1-1-11111-1-1−ii−ii-11−i−iii−i−i−i−i−i−iiiiiii-1-111-1-1-1-1-1-1111111ii−i−i−ii−ii−i−iii1-1i−iii−i−i1-1i−i-11
χ172222222-122222-122-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-12222002222-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000-1-122-1-1-1-122000000-1-10000
χ182222222-122222-122-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-122-2-2002222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000011-2-21111-2-2000000110000
χ192222222-122222-122-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-22200-2-2-2-211111111111100000000000000000000-1-122-1-1-1-1-2-2000000110000
χ202222222-122222-122-1-122222-1-12222-1-1-1-1-1-1-1-122-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-21111111111110000000000000000000011-2-2111122000000-1-10000
χ21222222-1222-1222222222-1-1-12-1-1-1-1-12-1222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100222200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1000022-1-1-1-1-1-10022000000-1-100
χ22222222-1222-1222222222-1-1-12-1-1-1-1-12-1222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022-2-20000000000000000-2-2-2-2111111111111000022-1-1-1-1-1-100-2-20000001100
χ23222222-1222-1222222222-1-1-12-1-1-1-1-12-1222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-22200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-10000-2-211111100-2-20000001100
χ24222222-1222-1222222222-1-1-12-1-1-1-1-12-1222222-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-2-2-20000000000000000-2-2-2-21111111111110000-2-21111110022000000-1-100
χ2522222-1222-12-1-12-1-122-1-122-1-122-1-1-1-122-1-12-1-1-1-1-1-12-1-122-12-1-1-12-1-1-1-1220022-1-1-1-122-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12222000000000000-1-1-1-1000000
χ2622222-1222-12-1-12-1-122-1-122-1-122-1-1-1-122-1-12-1-1-1-1-1-12-1-122-12-1-1-12-1-1-1-12200-2-2-1-1-1-122-1-1-1-122-1-1-1-11111-2-21111-2-21111-2-2-2-20000000000001111000000
χ2722222-1222-12-1-12-1-122-1-122-1-122-1-1-1-122-1-12-1-1-1-1-1-12-1-122-12-1-1-12-1-1-1-1-2-200221111-2-21111-2-21111-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-20000000000001111000000
χ2822222-1222-12-1-12-1-122-1-122-1-122-1-1-1-122-1-12-1-1-1-1-1-12-1-122-12-1-1-12-1-1-1-1-2-200-2-21111-2-21111-2-211111111-2-21111-2-211112222000000000000-1-1-1-1000000
χ292222-2222-222-2-22-2-2222222222-2-2-2222-2-2-2-2-2-22222-2-2-2222-2-2-22-2-2-222000000000000000000000000000000000000002-22-20000000000002-22-2000000
χ302222-2222-222-2-22-2-2222222222-2-2-2222-2-2-2-2-2-22222-2-2-2222-2-2-22-2-2-22200000000000000000000000000000000000000-22-22000000000000-22-22000000
χ312222-2-122-2-121121122-1-122-1-12-211-1-12-211-211-1-1-1-1-21122-1-211-1-211-1-10000003−33−30033−3−30033−3−33−33−30033−3−30033−3−32-22-2000000000000-11-11000000
χ322222-2-122-2-121121122-1-122-1-12-211-1-12-211-211-1-1-1-1-21122-1-211-1-211-1-10000003−33−30033−3−30033−3−3−33−3300−3−33300−3−333-22-220000000000001-11-1000000
χ332222-2-122-2-121121122-1-122-1-12-211-1-12-211-211-1-1-1-1-21122-1-211-1-211-1-1000000−33−3300−3−33300−3−3333−33−30033−3−30033−3−3-22-220000000000001-11-1000000
χ342222-2-122-2-121121122-1-122-1-12-211-1-12-211-211-1-1-1-1-21122-1-211-1-211-1-1000000−33−3300−3−33300−3−333−33−3300−3−33300−3−3332-22-2000000000000-11-11000000
χ3522-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2000000000000000000000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000
χ3622-2-22222-222222-2-2-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-200000000000000000000000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000
χ3722-2-22-122-2-12-1-1211-2-211-2-2-1-122-1-1-1-122-1-1-2111111-211-2-2-12-1-1-1-21111000000−i3i3i3−i300−i3−i3i3i300i3i3−i3−i33−3−330033−3−300−3−333−2i2i2i−2i000000000000i−i−ii000000
χ3822-2-22-122-2-12-1-1211-2-211-2-2-1-122-1-1-1-122-1-1-2111111-211-2-2-12-1-1-1-21111000000−i3i3i3−i300−i3−i3i3i300i3i3−i3−i3−333−300−3−3330033−3−32i−2i−2i2i000000000000−iii−i000000
χ3922-2-22-122-2-12-1-1211-2-211-2-2-1-122-1-1-1-122-1-1-2111111-211-2-2-12-1-1-1-21111000000i3−i3−i3i300i3i3−i3−i300−i3−i3i3i33−3−330033−3−300−3−3332i−2i−2i2i000000000000−iii−i000000
χ4022-2-22-122-2-12-1-1211-2-211-2-2-1-122-1-1-1-122-1-1-2111111-211-2-2-12-1-1-1-21111000000i3−i3−i3i300i3i3−i3−i300−i3−i3i3i3−333−300−3−3330033−3−3−2i2i2i−2i000000000000i−i−ii000000
χ4122-2-2-222-1222-2-2-12211-2-2-2-22-1-1-2-2-22-1-1111-1-1-1-2-21122211-1111-1-1-1-1112i−2i2i−2i002i2i−2i−2i−i−i−i−i−i−iiiiiii00000000000000000000−ii2i−2i−i−iii2-2000000-110000
χ4222-2-2-222-1222-2-2-12211-2-2-2-22-1-1-2-2-22-1-1111-1-1-1-2-21122211-1111-1-1-1-1112i−2i−2i2i002i2i−2i−2i−i−i−i−i−i−iiiiiii00000000000000000000i−i−2i2iii−i−i-220000001-10000
χ4322-2-2-222-1222-2-2-12211-2-2-2-22-1-1-2-2-22-1-1111-1-1-1-2-21122211-1111-1-1-1-111−2i2i2i−2i00−2i−2i2i2iiiiiii−i−i−i−i−i−i00000000000000000000−ii2i−2i−i−iii-220000001-10000
χ4422-2-2-222-1222-2-2-12211-2-2-2-22-1-1-2-2-22-1-1111-1-1-1-2-21122211-1111-1-1-1-111−2i2i−2i2i00−2i−2i2i2iiiiiii−i−i−i−i−i−i00000000000000000000i−i−2i2iii−i−i2-2000000-110000
χ4522-2-2-22-1222-1-2-2222-2-2-2-211-12-1111-12-1-2-2-222211-2-2-1-1-111-1111-1-1-1-111002i−2i2-2000000000000000022-2-2-1-1-1-1-1-111111100002i−2i−ii−i−iii002i−2i000000−ii00
χ4622-2-2-22-1222-1-2-2222-2-2-2-211-12-1111-12-1-2-2-222211-2-2-1-1-111-1111-1-1-1-111002i−2i-220000000000000000-2-222111111-1-1-1-1-1-100002i−2i−ii−i−iii00−2i2i000000i−i00
χ4722-2-2-22-1222-1-2-2222-2-2-2-211-12-1111-12-1-2-2-222211-2-2-1-1-111-1111-1-1-1-11100−2i2i2-2000000000000000022-2-2-1-1-1-1-1-11111110000−2i2ii−iii−i−i00−2i2i000000i−i00
χ4822-2-2-22-1222-1-2-2222-2-2-2-211-12-1111-12-1-2-2-222211-2-2-1-1-111-1111-1-1-1-11100−2i2i-220000000000000000-2-222111111-1-1-1-1-1-10000−2i2ii−iii−i−i002i−2i000000−ii00
χ4922-2-2-2-1222-12112-1-1-2-211-2-2-1-12-211-1-12-2112-1-111112-1-1-2-2-1-211-12-1-1112i−2i002-2−i−iii2i2i−i−i−i−i−2i−2iiiii-1-11122-1-1-1-1-2-211112i2i−2i−2i000000000000−i−iii000000
χ5022-2-2-2-1222-12112-1-1-2-211-2-2-1-12-211-1-12-2112-1-111112-1-1-2-2-1-211-12-1-1112i−2i00-22−i−iii2i2i−i−i−i−i−2i−2iiiii11-1-1-2-2111122-1-1-1-1−2i−2i2i2i000000000000ii−i−i000000
χ5122-2-2-2-1222-12112-1-1-2-211-2-2-1-12-211-1-12-2112-1-111112-1-1-2-2-1-211-12-1-111−2i2i002-2ii−i−i−2i−2iiiii2i2i−i−i−i−i-1-11122-1-1-1-1-2-21111−2i−2i2i2i000000000000ii−i−i000000
χ5222-2-2-2-1222-12112-1-1-2-211-2-2-1-12-211-1-12-2112-1-111112-1-1-2-2-1-211-12-1-111−2i2i00-22ii−i−i−2i−2iiiii2i2i−i−i−i−i11-1-1-2-2111122-1-1-1-12i2i−2i−2i000000000000−i−iii000000
χ53444444-2-244-244-244-2-244-2-2-2-21-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2111111111111004400000000000000000000000000000000000000-2-2-2-2111100000000000000
χ54444444-2-244-244-244-2-244-2-2-2-21-2-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2-211111111111100-4-4000000000000000000000000000000000000002222-1-1-1-100000000000000
χ5544444-24-24-24-2-2-2-2-2-2-2-2-244-21-24-2-2-21-2-211-211-2-2114-2-2-2-21-2111-21111440000-2-2-2-2-2-21111-2-21111000000000000000000000000000000000000000000
χ5644444-24-24-24-2-2-2-2-2-2-2-2-244-21-24-2-2-21-2-211-211-2-2114-2-2-2-21-2111-21111-4-40000222222-1-1-1-122-1-1-1-1000000000000000000000000000000000000000000
χ5744444-2-244-2-2-2-24-2-244-2-2-2-21-2-2-2111-2-24-2-24-2-211-2-2-211-2-21-2111-211110000440000000000000000-2-2-2-2-2-21111-2-2111100000000000000000000000000
χ5844444-2-244-2-2-2-24-2-244-2-2-2-21-2-2-2111-2-24-2-24-2-211-2-2-211-2-21-2111-211110000-4-40000000000000000222222-1-1-1-122-1-1-1-100000000000000000000000000
χ594444-444-2-444-4-4-2-4-4-2-244444-2-2-4-4-44-2-222222244-2-2-4-4-4-2-2-2222-2222-2-20000000000000000000000000000000000000000000000000000000000000000
χ604444-44-24-44-2-4-44-4-44444-2-2-24-2222-24-2-4-4-4-4-4-4-2-244222-2-2-2222-2222-2-20000000000000000000000000000000000000000000000000000000000000000
χ614444-44-2-2-44-2-4-4-2-4-4-2-244-2-2-2-21222-2-21222222-2-2-2-2222111-1-1-11-1-1-11100000000000000000000000000000000000000000000003-33-300000000000000
χ624444-44-2-2-44-2-4-4-2-4-4-2-244-2-2-2-21222-2-21222222-2-2-2-2222111-1-1-11-1-1-1110000000000000000000000000000000000000000000000-33-3300000000000000
χ634444-4-24-2-4-2422-222-2-2-2-244-21-2-422-21-22-1-12-1-1-2-211-422-2-212-1-112-1-11100000023−2323−2300−3−33300−3−333000000000000000000000000000000000000000000
χ644444-4-24-2-4-2422-222-2-2-2-244-21-2-422-21-22-1-12-1-1-2-211-422-2-212-1-112-1-111000000−2323−23230033−3−30033−3−3000000000000000000000000000000000000000000
χ654444-4-2-24-4-2-22242244-2-2-2-21-2-22-1-11-2-2-422-42211-2-22-1-1-2-212-1-112-1-111000000000000000000000023−2323−2300−3−33300−3−33300000000000000000000000000
χ664444-4-2-24-4-2-22242244-2-2-2-21-2-22-1-11-2-2-422-42211-2-22-1-1-2-212-1-112-1-1110000000000000000000000−2323−23230033−3−30033−3−300000000000000000000000000
χ6744-4-4444-2-44444-2-4-422-4-4-4-44-2-24444-2-2-2-2-2222-4-422-4-4-422-2-2-2-2-2222220000000000000000000000000000000000000000000000000000000000000000
χ6844-4-444-24-44-2444-4-4-4-4-4-422-24-2-2-2-2-24-2444-4-4-422-4-422222-2-2-2-2-2222220000000000000000000000000000000000000000000000000000000000000000
χ6944-4-444-2-2-44-244-2-4-422-4-422-2-21-2-2-2-2-21-2-2-22222222222-1-111111-1-1-1-1-100000000000000000000000000000000000000000000003i−3i−3i3i00000000000000
χ7044-4-444-2-2-44-244-2-4-422-4-422-2-21-2-2-2-2-21-2-2-22222222222-1-111111-1-1-1-1-10000000000000000000000000000000000000000000000−3i3i3i−3i00000000000000
χ7144-4-44-24-2-4-24-2-2-2222222-4-4-21-24-2-2-21-2-2112-1-122-1-1-422221-21112-1-1-1-1000000−2i32i32i3−2i300i3i3−i3−i300−i3−i3i3i3000000000000000000000000000000000000000000
χ7244-4-44-24-2-4-24-2-2-2222222-4-4-21-24-2-2-21-2-2112-1-122-1-1-422221-21112-1-1-1-10000002i3−2i3−2i32i300−i3−i3i3i300i3i3−i3−i3000000000000000000000000000000000000000000
χ7344-4-44-2-24-4-2-2-2-2422-4-422221-2-2-2111-2-24-2-2-422-1-1222-1-1221-21112-1-1-1-1000000000000000000000023−23−232300−3−3330033−3−300000000000000000000000000
χ7444-4-44-2-24-4-2-2-2-2422-4-422221-2-2-2111-2-24-2-2-422-1-1222-1-1221-21112-1-1-1-10000000000000000000000−232323−230033−3−300−3−33300000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.