Finite Group Databasebeta

← Group #13155719

Character table — Group #13155719

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222222222224444444444444444444444666666666666888888888888121212121212121212121212121212121212121212121212242424242424242424242424363636363636363636363636363636363636108108
order12223334466666666633366666666612121212121212121212444412121212121212123666121212121212121244441212121212121212121212121212121212121212121212121212121212121212222266666666882424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1
χ911-1-11111-1111-1-1-1-1-1-1111-1-1111-1-1-1-111-1-1-111-1-11ii−i−iiiii−i−i−i−i1-1-1111-1-111-1-1i−ii−iii−i−iii−i−iii−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i1-11-111-1-111-1-11-111-1-1i−i
χ1011-1-11111-1111-1-1-1-1-1-1111-1-1111-1-1-1-111-1-1-111-1-11ii−i−iiiii−i−i−i−i1-1-1111-1-111-1-1i−i−iiii−i−iii−i−i−i−iiiiiii−i−i−i−ii−i−iiii−i−i−i−iii1-1-1111-1-1-1-111-11-1-111−ii
χ1111-1-11111-1111-1-1-1-1-1-1111-1-1111-1-1-1-111-1-1-111-1-11ii−i−iiiii−i−i−i−i1-1-1111-1-111-1-1−iii−iii−i−i−i−iiiii−i−iiiii−i−i−i−i−iii−i−i−iiiii−i−i-111-1-1-11111-1-1-11-1-111−ii
χ1211-1-11111-1111-1-1-1-1-1-1111-1-1111-1-1-1-111-1-1-111-1-11ii−i−iiiii−i−i−i−i1-1-1111-1-111-1-1−ii−iiii−i−i−i−iii−i−iiiiiii−i−i−i−i−ii−ii−i−iii−i−iii-11-11-1-111-1-1111-111-1-1i−i
χ1311-1-11111-1111-1-1-1-1-1-1111-1-1111-1-1-1-111-1-1-111-1-11−i−iii−i−i−i−iiiii1-1-1111-1-111-1-1i−ii−i−i−iiiii−i−iii−i−i−i−i−i−iiiiii−ii−iii−i−iii−i−i-11-11-1-111-1-1111-111-1-1−ii
χ1411-1-11111-1111-1-1-1-1-1-1111-1-1111-1-1-1-111-1-1-111-1-11−i−iii−i−i−i−iiiii1-1-1111-1-111-1-1i−i−ii−i−iiiii−i−i−i−iii−i−i−i−iiiiii−i−iiii−i−i−i−iii-111-1-1-11111-1-1-11-1-111i−i
χ1511-1-11111-1111-1-1-1-1-1-1111-1-1111-1-1-1-111-1-1-111-1-11−i−iii−i−i−i−iiiii1-1-1111-1-111-1-1−iii−i−i−iii−i−iiiii−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i1-1-1111-1-1-1-111-11-1-111i−i
χ1611-1-11111-1111-1-1-1-1-1-1111-1-1111-1-1-1-111-1-1-111-1-11−i−iii−i−i−i−iiiii1-1-1111-1-111-1-1−ii−ii−i−iii−i−iii−i−iii−i−i−i−iiiii−ii−ii−i−iii−i−iii1-11-111-1-111-1-11-111-1-1−ii
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22-22-222-2-222-2-22222-2-2-2-2-2-2-2-200002-22-20000000022-2-222-2-200000000000000000000000000000000
χ182222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-2-22-22-2-222-2-2222222-2-2-2-2-2-2-2-20000-22-2200000000-2-222-2-22200000000000000000000000000000000
χ19222222-12222-12-1222-12-1-12-12-1-1-1-12-12-122-1-1-1-1-12222222-1-122-1-1-1-1-1-12-12-1-1-1-1-10022-12-120000-1-1-1-1-1-1-1-1-1-1-1-100220000-1-1-1-100220000-1-1-1-100000000
χ20222222-12222-12-1222-12-1-12-12-1-1-1-12-12-122-1-1-1-1-12222222-1-122-1-1-1-1-1-12-12-1-1-1-1-100-2-2-12-1200001111-1-1-1-1-1-1-1-100-2-20000111100-2-20000111100000000
χ21222222-12222-12-1222-12-1-12-12-1-1-1-12-12-122-1-1-1-1-12-2-2-2-2-2-211-2-211-1-1-1-12-12-1-1-1-1-100221-21-20000-1-1-1-11111111100220000-1-1-1-100-2-20000111100000000
χ22222222-12222-12-1222-12-1-12-12-1-1-1-12-12-122-1-1-1-1-12-2-2-2-2-2-211-2-211-1-1-1-12-12-1-1-1-1-100-2-21-21-2000011111111111100-2-20000111100220000-1-1-1-100000000
χ23222222-1-2-222-12-1222-12-1-12-12-1-1-1-12-1-21-2-211111-22-22-222112211-1-1-1-1-21-2111110000-1-2-1-20000−i3i3−i3i3-1-111-1-11100000000−i3i3−i3i300000000−i3i3−i3i300000000
χ24222222-1-2-222-12-1222-12-1-12-12-1-1-1-12-1-21-2-211111-22-22-222112211-1-1-1-1-21-2111110000-1-2-1-20000i3−i3i3−i3-1-111-1-11100000000i3−i3i3−i300000000i3−i3i3−i300000000
χ25222222-1-2-222-12-1222-12-1-12-12-1-1-1-12-1-21-2-211111-2-22-22-2-2-1-1-2-2-1-1-1-1-1-1-21-211111000012120000−i3i3−i3i311-1-111-1-100000000−i3i3−i3i300000000i3−i3i3−i300000000
χ26222222-1-2-222-12-1222-12-1-12-12-1-1-1-12-1-21-2-211111-2-22-22-2-2-1-1-2-2-1-1-1-1-1-1-21-211111000012120000i3−i3i3−i311-1-111-1-100000000i3−i3i3−i300000000−i3i3−i3i300000000
χ2722222-12222-12-1222-12-12-1-12-12-1-1-1-12-122-12-1-1-1-122222-1-122-1-122-1-1-1-1-12-12-1-1-1-122002-12-1-1-1-1-10000-1-1-1-1-1-1-1-12200-1-1-1-100002200-1-1-1-1000000000000
χ2822222-12222-12-1222-12-12-1-12-12-1-1-1-12-122-12-1-1-1-122222-1-122-1-122-1-1-1-1-12-12-1-1-1-1-2-2002-12-111110000-1-1-1-1-1-1-1-1-2-20011110000-2-2001111000000000000
χ2922222-12222-12-1222-12-12-1-12-12-1-1-1-12-122-12-1-1-1-12-2-2-2-211-2-211-2-2-1-1-1-1-12-12-1-1-1-12200-21-21-1-1-1-10000111111112200-1-1-1-10000-2-2001111000000000000
χ3022222-12222-12-1222-12-12-1-12-12-1-1-1-12-122-12-1-1-1-12-2-2-2-211-2-211-2-2-1-1-1-1-12-12-1-1-1-1-2-200-21-211111000011111111-2-200111100002200-1-1-1-1000000000000
χ3122222-12-2-22-12-1222-12-12-1-12-12-1-1-1-121-2-21-21111-22-22-2-1-1-2-2-1-1-2-2-1-1-1-11-21-2111100002121−i3i3−i3i30000-1-111-1-1110000−i3i3−i3i300000000−i3i3−i3i3000000000000
χ3222222-12-2-22-12-1222-12-12-1-12-12-1-1-1-121-2-21-21111-22-22-2-1-1-2-2-1-1-2-2-1-1-1-11-21-2111100002121i3−i3i3−i30000-1-111-1-1110000i3−i3i3−i300000000i3−i3i3−i3000000000000
χ3322222-12-2-22-12-1222-12-12-1-12-12-1-1-1-121-2-21-21111-2-22-2211221122-1-1-1-11-21-211110000-2-1-2-1−i3i3−i3i3000011-1-111-1-10000−i3i3−i3i300000000i3−i3i3−i3000000000000
χ3422222-12-2-22-12-1222-12-12-1-12-12-1-1-1-121-2-21-21111-2-22-2211221122-1-1-1-11-21-211110000-2-1-2-1i3−i3i3−i3000011-1-111-1-10000i3−i3i3−i300000000−i3i3−i3i3000000000000
χ352222-12222-12222-1-122-1-12-1-1-1-1222-1-122-1222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-100000000000022-1-1-1-100
χ362222-12222-12222-1-122-1-12-1-1-1-1222-1-122-1222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-122-2-200002222-2-2-2-200000000-1-111-1-1-1-11111000000000000-2-2111100
χ372222-12222-12222-1-122-1-12-1-1-1-1222-1-122-1222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000-2-2-2-222220000000011-1-11111-1-1-1-1000000000000-2-2111100
χ382222-12222-12222-1-122-1-12-1-1-1-1222-1-122-1222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-2-2-2-2-20000000011111111111100000000000022-1-1-1-100
χ3922-2-2222-22222-2-2-2-2-2-2222-2-2222-2-2-2-2-2-2222-2-222-22i−2i−2i2i2i2i−2i−2i−2i−2i2i2i2-2-22-2-222-2-22200002i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ4022-2-2222-22222-2-2-2-2-2-2222-2-2222-2-2-2-2-2-2222-2-222-2−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i2-2-22-2-222-2-2220000−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ4122-2-222-12-222-1-21-2-2-212-1-1-212-1-111-212-1-2-21-1-11122i2i−2i−2i2i2i−i−i−2i−2iii-111-12-1-21-1-111002i−2i−i2ii−2i0000−i−iii−i−i−i−iiiii002i−2i0000−i−iii002-20000-1-11100000000
χ4222-2-222-12-222-1-21-2-2-212-1-1-212-1-111-212-1-2-21-1-11122i2i−2i−2i2i2i−i−i−2i−2iii-111-12-1-21-1-11100−2i2i−i2ii−2i0000ii−i−i−i−i−i−iiiii00−2i2i0000ii−i−i00-22000011-1-100000000
χ4322-2-222-12-222-1-21-2-2-212-1-1-212-1-111-212-1-2-21-1-1112−2i−2i2i2i−2i−2iii2i2i−i−i-111-12-1-21-1-111002i−2ii−2i−i2i0000−i−iiiiiii−i−i−i−i002i−2i0000−i−iii00-22000011-1-100000000
χ4422-2-222-12-222-1-21-2-2-212-1-1-212-1-111-212-1-2-21-1-1112−2i−2i2i2i−2i−2iii2i2i−i−i-111-12-1-21-1-11100−2i2ii−2i−i2i0000ii−i−iiiii−i−i−i−i00−2i2i0000ii−i−i002-20000-1-11100000000
χ4522-2-222-1-2222-1-21-2-2-212-1-1-212-1-111-21-2122-111-1-1-22i−2i−2i2i2i2iii−2i−2i−i−i-111-1-212-111-1-10000−i−2ii2i00003−3−33−i−iiiii−i−i000000003−3−3300000000−i3i3i3−i300000000
χ4622-2-222-1-2222-1-21-2-2-212-1-1-212-1-111-21-2122-111-1-1-22i−2i−2i2i2i2iii−2i−2i−i−i-111-1-212-111-1-10000−i−2ii2i0000−333−3−i−iiiii−i−i00000000−333−300000000i3−i3−i3i300000000
χ4722-2-222-1-2222-1-21-2-2-212-1-1-212-1-111-21-2122-111-1-1-2−2i2i2i−2i−2i−2i−i−i2i2iii-111-1-212-111-1-10000i2i−i−2i00003−3−33ii−i−i−i−iii000000003−3−3300000000i3−i3−i3i300000000
χ4822-2-222-1-2222-1-21-2-2-212-1-1-212-1-111-21-2122-111-1-1-2−2i2i2i−2i−2i−2i−i−i2i2iii-111-1-212-111-1-10000i2i−i−2i0000−333−3ii−i−i−i−iii00000000−333−300000000−i3i3i3−i300000000
χ4922-2-22-122-22-121-2-2-21-2-12-11-2-12-1111-2-12-21-2-1-11122i2i−2i−2i−i−i2i2iii−2i−2i-111-1-121-2-1-1112i−2i002i−i−2ii−i−iii0000−i−i−i−iiiii2i−2i00−i−iii00002-200-1-111000000000000
χ5022-2-22-122-22-121-2-2-21-2-12-11-2-12-1111-2-12-21-2-1-11122i2i−2i−2i−i−i2i2iii−2i−2i-111-1-121-2-1-111−2i2i002i−i−2iiii−i−i0000−i−i−i−iiiii−2i2i00ii−i−i0000-220011-1-1000000000000
χ5122-2-22-122-22-121-2-2-21-2-12-11-2-12-1111-2-12-21-2-1-1112−2i−2i2i2iii−2i−2i−i−i2i2i-111-1-121-2-1-1112i−2i00−2ii2i−i−i−iii0000iiii−i−i−i−i2i−2i00−i−iii0000-220011-1-1000000000000
χ5222-2-22-122-22-121-2-2-21-2-12-11-2-12-1111-2-12-21-2-1-1112−2i−2i2i2iii−2i−2i−i−i2i2i-111-1-121-2-1-111−2i2i00−2ii2i−iii−i−i0000iiii−i−i−i−i−2i2i00ii−i−i00002-200-1-111000000000000
χ5322-2-22-12-222-121-2-2-21-2-12-11-2-12-1111-21-22-1211-1-1-22i−2i−2i2i−i−i−2i−2iii2i2i-111-11-2-1211-1-100002ii−2i−i3−3−330000−i−iiiii−i−i00003−3−3300000000−i3i3i3−i3000000000000
χ5422-2-22-12-222-121-2-2-21-2-12-11-2-12-1111-21-22-1211-1-1-22i−2i−2i2i−i−i−2i−2iii2i2i-111-11-2-1211-1-100002ii−2i−i−333−30000−i−iiiii−i−i0000−333−300000000i3−i3−i3i3000000000000
χ5522-2-22-12-222-121-2-2-21-2-12-11-2-12-1111-21-22-1211-1-1-2−2i2i2i−2iii2i2i−i−i−2i−2i-111-11-2-1211-1-10000−2i−i2ii3−3−330000ii−i−i−i−iii00003−3−3300000000i3−i3−i3i3000000000000
χ5622-2-22-12-222-121-2-2-21-2-12-11-2-12-1111-21-22-1211-1-1-2−2i2i2i−2iii2i2i−i−i−2i−2i-111-11-2-1211-1-10000−2i−i2ii−333−30000ii−i−i−i−iii0000−333−300000000−i3i3i3−i3000000000000
χ5722-2-2-1222-2-122-2-211-2-2-1-1211-1-12-2-211221-2-222-2-2-1000000000000-111-1-1-111-1-1112i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i00000000−ii−ii−i−iii−i−iii0000000000002-2-1-11100
χ5822-2-2-1222-2-122-2-211-2-2-1-1211-1-12-2-211221-2-222-2-2-1000000000000-111-1-1-111-1-1112i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000−iii−i−i−iiiii−i−i000000000000-2211-1-100
χ5922-2-2-1222-2-122-2-211-2-2-1-1211-1-12-2-211221-2-222-2-2-1000000000000-111-1-1-111-1-111−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000i−i−iiii−i−i−i−iii000000000000-2211-1-100
χ6022-2-2-1222-2-122-2-211-2-2-1-1211-1-12-2-211221-2-222-2-2-1000000000000-111-1-1-111-1-111−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i00000000i−ii−iii−i−iii−i−i0000000000002-2-1-11100
χ6144444-2-2444-2-2-2-244-2-2-2-21-2-2-2-2111-2-2-2-24-2-2111144444-2-2-2-2-2-2-2-21111-2-2-2-211110000-2-2-2-2000000001111111100000000000000000000000000000000
χ6244444-2-2444-2-2-2-244-2-2-2-21-2-2-2-2111-2-2-2-24-2-211114-4-4-4-4222222221111-2-2-2-211110000222200000000-1-1-1-1-1-1-1-100000000000000000000000000000000
χ6344444-2-2-4-44-2-2-2-244-2-2-2-21-2-2-2-2111-2-222-422-1-1-1-1-44-44-4-2-222-2-22211112222-1-1-1-10000-22-220000000011-1-111-1-100000000000000000000000000000000
χ6444444-2-2-4-44-2-2-2-244-2-2-2-21-2-2-2-2111-2-222-422-1-1-1-1-4-44-4422-2-222-2-211112222-1-1-1-100002-22-200000000-1-111-1-11100000000000000000000000000000000
χ654444-244-4-4-24444-2-244-2-24-2-2-2-2444-2-2-4-42-4-4-4-4-4-42000000000000-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ664444-24-244-24-24-2-2-24-2-21-2-21-21-2-2-2-214-2-24-2-2-2-2-2-20000000000001111-21-211111004400000000-2-2-2-20000000000-2-20000111100000000000000000000
χ674444-24-244-24-24-2-2-24-2-21-2-21-21-2-2-2-214-2-24-2-2-2-2-2-20000000000001111-21-21111100-4-40000000022220000000000220000-1-1-1-100000000000000000000
χ684444-24-2-4-4-24-24-2-2-24-2-21-2-21-21-2-2-2-21-422-422222200000000000011112-12-1-1-1-1-1000000000000−2i32i3−2i32i30000000000000000i3−i3i3−i300000000000000000000
χ694444-24-2-4-4-24-24-2-2-24-2-21-2-21-21-2-2-2-21-422-422222200000000000011112-12-1-1-1-1-10000000000002i3−2i32i3−2i30000000000000000−i3i3−i3i300000000000000000000
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χ1044-4-444-2-200-4222-2-44-22-2-212-222-1-11-22000003i−3i−3i3i000002i3−2i323−23−2i32i3−23231-11-100003i−3i−3i3i0000000000000000−i3i3−33i3−i33−300000000000000000000000000000000
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χ1064-4-444-2-200-4222-2-44-22-2-212-222-1-11-2200000−3i3i3i−3i000002i3−2i3−2323−2i32i323−231-11-10000−3i3i3i−3i0000000000000000−i3i33−3i3−i3−3300000000000000000000000000000000
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χ1108888-4-4-4-8-8-4-4-4-4-4-4-4-4-422222222222244444-2-2-2-24000000000000-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000
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χ1138-88-8-48-4004-8484-44-8-4-42-4-4-24-24-4442000000000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ1148-88-8-4-480044-8-4-8-44482-4-424-244-44-2-4000000000000000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ1158-88-8-4-4-400444-44-444-42222-2-2-2-22-2-22000006i−6i6i−6i0000000000000-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
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χ1178-8-88-48-4004-84-8-44-484-42-4424-244-4-4-200000000000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000
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Here i is the imaginary unit (i² = −1).