Finite Group Databasebeta

← Group #13155703

Character table — Group #13155703

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222222222224444444444444444444444666666666666888888888888121212121212121212121212121212121212121212121212242424242424242424242424363636363636363636363636363636363636108108
order1222333446666666663336666666661212121212121212121244441212121212121212366612121212121212124444121212121212121212121212121212121212121212121212121212121212121244448812121212121212122424242488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-11111111111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1111111111111-1-111-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-111
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
χ91-1-111111-11-1-1-1-1-1-111111-1-1111-1-1-1-1-111-1-111-1-11ii−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−i1-11-11-111-1-111-1-111-1-1i−i
χ101-1-111111-11-1-1-1-1-1-111111-1-1111-1-1-1-1-111-1-111-1-11ii−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−iii1-1-11-1111-1-1-1-111-1-111−ii
χ111-1-111111-11-1-1-1-1-1-111111-1-1111-1-1-1-1-111-1-111-1-11ii−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-111-1-11-1-11111-1-1-1-111−ii
χ121-1-111111-11-1-1-1-1-1-111111-1-1111-1-1-1-1-111-1-111-1-11ii−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-11-111-1-1-111-1-11111-1-1i−i
χ131-1-111111-11-1-1-1-1-1-111111-1-1111-1-1-1-1-111-1-111-1-11−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-11-111-1-1-111-1-11111-1-1−ii
χ141-1-111111-11-1-1-1-1-1-111111-1-1111-1-1-1-1-111-1-111-1-11−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-111-1-11-1-11111-1-1-1-111i−i
χ151-1-111111-11-1-1-1-1-1-111111-1-1111-1-1-1-1-111-1-111-1-11−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−i1-1-11-1111-1-1-1-111-1-111i−i
χ161-1-111111-11-1-1-1-1-1-111111-1-1111-1-1-1-1-111-1-111-1-11−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−iii1-11-11-111-1-111-1-111-1-1−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
χ19222222-12222-1222-12-12-1-12-12-1-1-1-12-122-12-1-1-1-1-12222222-1-122-1-1-1-1-1-12-12-1-1-1-1-10022-12-120000-1-1-1-1-1-1-1-1-1-1-1-100220000-1-1-1-10022000000-1-1-1-1000000
χ20222222-12222-1222-12-12-1-12-12-1-1-1-12-122-12-1-1-1-1-12222222-1-122-1-1-1-1-1-12-12-1-1-1-1-100-2-2-12-1200001111-1-1-1-1-1-1-1-100-2-20000111100-2-20000001111000000
χ21222222-12222-1222-12-12-1-12-12-1-1-1-12-122-12-1-1-1-1-12-2-2-2-2-2-211-2-211-1-1-1-12-12-1-1-1-1-100221-21-20000-1-1-1-11111111100220000-1-1-1-100-2-20000001111000000
χ22222222-12222-1222-12-12-1-12-12-1-1-1-12-122-12-1-1-1-1-12-2-2-2-2-2-211-2-211-1-1-1-12-12-1-1-1-1-100-2-21-21-2000011111111111100-2-2000011110022000000-1-1-1-1000000
χ23222222-1-2-222-1222-12-12-1-12-12-1-1-1-12-1-2-21-211111-22-22-222112211-1-1-1-1-21-2111110000-1-2-1-20000−i3i3−i3i3-1-111-1-11100000000−i3i3−i3i30000000000−i3i3−i3i3000000
χ24222222-1-2-222-1222-12-12-1-12-12-1-1-1-12-1-2-21-211111-22-22-222112211-1-1-1-1-21-2111110000-1-2-1-20000i3−i3i3−i3-1-111-1-11100000000i3−i3i3−i30000000000i3−i3i3−i3000000
χ25222222-1-2-222-1222-12-12-1-12-12-1-1-1-12-1-2-21-211111-2-22-22-2-2-1-1-2-2-1-1-1-1-1-1-21-211111000012120000−i3i3−i3i311-1-111-1-100000000−i3i3−i3i30000000000i3−i3i3−i3000000
χ26222222-1-2-222-1222-12-12-1-12-12-1-1-1-12-1-2-21-211111-2-22-22-2-2-1-1-2-2-1-1-1-1-1-1-21-211111000012120000i3−i3i3−i311-1-111-1-100000000i3−i3i3−i30000000000−i3i3−i3i3000000
χ2722222-12222-1222-12-12-12-1-12-12-1-1-1-122-12-12-1-1-1-122222-1-122-1-122-1-1-1-1-12-12-1-1-1-122002-12-1-1-1-1-10000-1-1-1-1-1-1-1-12200-1-1-1-10000220000-1-1-1-10000000000
χ2822222-12222-1222-12-12-12-1-12-12-1-1-1-122-12-12-1-1-1-122222-1-122-1-122-1-1-1-1-12-12-1-1-1-1-2-2002-12-111110000-1-1-1-1-1-1-1-1-2-20011110000-2-2000011110000000000
χ2922222-12222-1222-12-12-12-1-12-12-1-1-1-122-12-12-1-1-1-12-2-2-2-211-2-211-2-2-1-1-1-1-12-12-1-1-1-12200-21-21-1-1-1-10000111111112200-1-1-1-10000-2-2000011110000000000
χ3022222-12222-1222-12-12-12-1-12-12-1-1-1-122-12-12-1-1-1-12-2-2-2-211-2-211-2-2-1-1-1-1-12-12-1-1-1-1-2-200-21-211111000011111111-2-20011110000220000-1-1-1-10000000000
χ3122222-12-2-22-1222-12-12-12-1-12-12-1-1-1-12-21-21-21111-22-22-2-1-1-2-2-1-1-2-2-1-1-1-11-21-2111100002121−i3i3−i3i30000-1-111-1-1110000−i3i3−i3i30000000000−i3i3−i3i30000000000
χ3222222-12-2-22-1222-12-12-12-1-12-12-1-1-1-12-21-21-21111-22-22-2-1-1-2-2-1-1-2-2-1-1-1-11-21-2111100002121i3−i3i3−i30000-1-111-1-1110000i3−i3i3−i30000000000i3−i3i3−i30000000000
χ3322222-12-2-22-1222-12-12-12-1-12-12-1-1-1-12-21-21-21111-2-22-2211221122-1-1-1-11-21-211110000-2-1-2-1−i3i3−i3i3000011-1-111-1-10000−i3i3−i3i30000000000i3−i3i3−i30000000000
χ3422222-12-2-22-1222-12-12-12-1-12-12-1-1-1-12-21-21-21111-2-22-2211221122-1-1-1-11-21-211110000-2-1-2-1i3−i3i3−i3000011-1-111-1-10000i3−i3i3−i30000000000−i3i3−i3i30000000000
χ352222-12222-122-1-12222-1-12-1-1-1-1222-1-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-100002200000000-1-1-1-100
χ362222-12222-122-1-12222-1-12-1-1-1-1222-1-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-122-2-200002222-2-2-2-200000000-1-111-1-1-1-111110000-2-200000000111100
χ372222-12222-122-1-12222-1-12-1-1-1-1222-1-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000-2-2-2-222220000000011-1-11111-1-1-1-10000-2-200000000111100
χ382222-12222-122-1-12222-1-12-1-1-1-1222-1-1-122222222-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-2-2-2-2-20000000011111111111100002200000000-1-1-1-100
χ392-2-22222-222-2-2-2-2-2-222222-2-2222-2-2-2-22-2-222-2-222-22i−2i−2i2i2i2i−2i−2i−2i−2i2i2i2-2-22-2-222-2-22200002i−2i−2i2i000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ402-2-22222-222-2-2-2-2-2-222222-2-2222-2-2-2-22-2-222-2-222-2−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i2-2-22-2-222-2-2220000−2i2i2i−2i00000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ412-2-2222-12-22-21-2-2-212-12-1-1-212-1-111-21-22-1-21-1-11122i2i−2i−2i2i2i−i−i−2i−2iii-111-12-1-21-1-111002i−2i−i2ii−2i0000−i−iii−i−i−i−iiiii002i−2i0000−i−iii002-2000000-1-111000000
χ422-2-2222-12-22-21-2-2-212-12-1-1-212-1-111-21-22-1-21-1-11122i2i−2i−2i2i2i−i−i−2i−2iii-111-12-1-21-1-11100−2i2i−i2ii−2i0000ii−i−i−i−i−i−iiiii00−2i2i0000ii−i−i00-2200000011-1-1000000
χ432-2-2222-12-22-21-2-2-212-12-1-1-212-1-111-21-22-1-21-1-1112−2i−2i2i2i−2i−2iii2i2i−i−i-111-12-1-21-1-111002i−2ii−2i−i2i0000−i−iiiiiii−i−i−i−i002i−2i0000−i−iii00-2200000011-1-1000000
χ442-2-2222-12-22-21-2-2-212-12-1-1-212-1-111-21-22-1-21-1-1112−2i−2i2i2i−2i−2iii2i2i−i−i-111-12-1-21-1-11100−2i2ii−2i−i2i0000ii−i−iiiii−i−i−i−i00−2i2i0000ii−i−i002-2000000-1-111000000
χ452-2-2222-1-222-21-2-2-212-12-1-1-212-1-111-212-212-111-1-1-22i−2i−2i2i2i2iii−2i−2i−i−i-111-1-212-111-1-10000−i−2ii2i00003−3−33−i−iiiii−i−i000000003−3−330000000000−i3i3i3−i3000000
χ462-2-2222-1-222-21-2-2-212-12-1-1-212-1-111-212-212-111-1-1-22i−2i−2i2i2i2iii−2i−2i−i−i-111-1-212-111-1-10000−i−2ii2i0000−333−3−i−iiiii−i−i00000000−333−30000000000i3−i3−i3i3000000
χ472-2-2222-1-222-21-2-2-212-12-1-1-212-1-111-212-212-111-1-1-2−2i2i2i−2i−2i−2i−i−i2i2iii-111-1-212-111-1-10000i2i−i−2i00003−3−33ii−i−i−i−iii000000003−3−330000000000i3−i3−i3i3000000
χ482-2-2222-1-222-21-2-2-212-12-1-1-212-1-111-212-212-111-1-1-2−2i2i2i−2i−2i−2i−i−i2i2iii-111-1-212-111-1-10000i2i−i−2i0000−333−3ii−i−i−i−iii00000000−333−30000000000−i3i3i3−i3000000
χ492-2-222-122-221-2-2-21-2-12-12-11-2-12-1111-2-2-121-2-1-11122i2i−2i−2i−i−i2i2iii−2i−2i-111-1-121-2-1-1112i−2i002i−i−2ii−i−iii0000−i−i−i−iiiii2i−2i00−i−iii00002-20000-1-1110000000000
χ502-2-222-122-221-2-2-21-2-12-12-11-2-12-1111-2-2-121-2-1-11122i2i−2i−2i−i−i2i2iii−2i−2i-111-1-121-2-1-111−2i2i002i−i−2iiii−i−i0000−i−i−i−iiiii−2i2i00ii−i−i0000-22000011-1-10000000000
χ512-2-222-122-221-2-2-21-2-12-12-11-2-12-1111-2-2-121-2-1-1112−2i−2i2i2iii−2i−2i−i−i2i2i-111-1-121-2-1-1112i−2i00−2ii2i−i−i−iii0000iiii−i−i−i−i2i−2i00−i−iii0000-22000011-1-10000000000
χ522-2-222-122-221-2-2-21-2-12-12-11-2-12-1111-2-2-121-2-1-1112−2i−2i2i2iii−2i−2i−i−i2i2i-111-1-121-2-1-111−2i2i00−2ii2i−iii−i−i0000iiii−i−i−i−i−2i2i00ii−i−i00002-20000-1-1110000000000
χ532-2-222-12-2221-2-2-21-2-12-12-11-2-12-1111-221-2-1211-1-1-22i−2i−2i2i−i−i−2i−2iii2i2i-111-11-2-1211-1-100002ii−2i−i3−3−330000−i−iiiii−i−i00003−3−330000000000−i3i3i3−i30000000000
χ542-2-222-12-2221-2-2-21-2-12-12-11-2-12-1111-221-2-1211-1-1-22i−2i−2i2i−i−i−2i−2iii2i2i-111-11-2-1211-1-100002ii−2i−i−333−30000−i−iiiii−i−i0000−333−30000000000i3−i3−i3i30000000000
χ552-2-222-12-2221-2-2-21-2-12-12-11-2-12-1111-221-2-1211-1-1-2−2i2i2i−2iii2i2i−i−i−2i−2i-111-11-2-1211-1-10000−2i−i2ii3−3−330000ii−i−i−i−iii00003−3−330000000000i3−i3−i3i30000000000
χ562-2-222-12-2221-2-2-21-2-12-12-11-2-12-1111-221-2-1211-1-1-2−2i2i2i−2iii2i2i−i−i−2i−2i-111-11-2-1211-1-10000−2i−i2ii−333−30000ii−i−i−i−iii0000−333−30000000000−i3i3i3−i30000000000
χ572-2-22-1222-2-1-2-211-2-222-1-1211-1-12-2-211122-2-222-2-2-1000000000000-111-1-1-111-1-1112i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i00000000−ii−ii−i−iii−i−iii00002-200000000-1-11100
χ582-2-22-1222-2-1-2-211-2-222-1-1211-1-12-2-211122-2-222-2-2-1000000000000-111-1-1-111-1-1112i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000−iii−i−i−iiiii−i−i0000-220000000011-1-100
χ592-2-22-1222-2-1-2-211-2-222-1-1211-1-12-2-211122-2-222-2-2-1000000000000-111-1-1-111-1-111−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000i−i−iiii−i−i−i−iii0000-220000000011-1-100
χ602-2-22-1222-2-1-2-211-2-222-1-1211-1-12-2-211122-2-222-2-2-1000000000000-111-1-1-111-1-111−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i00000000i−ii−iii−i−iii−i−i00002-200000000-1-11100
χ6144444-2-2444-2-244-2-2-2-2-2-21-2-2-2-2111-2-24-2-2-2-2111144444-2-2-2-2-2-2-2-21111-2-2-2-211110000-2-2-2-2000000001111111100000000000000000000000000000000
χ6244444-2-2444-2-244-2-2-2-2-2-21-2-2-2-2111-2-24-2-2-2-211114-4-4-4-4222222221111-2-2-2-211110000222200000000-1-1-1-1-1-1-1-100000000000000000000000000000000
χ6344444-2-2-4-44-2-244-2-2-2-2-2-21-2-2-2-2111-2-2-42222-1-1-1-1-44-44-4-2-222-2-22211112222-1-1-1-10000-22-220000000011-1-111-1-100000000000000000000000000000000
χ6444444-2-2-4-44-2-244-2-2-2-2-2-21-2-2-2-2111-2-2-42222-1-1-1-1-4-44-4422-2-222-2-211112222-1-1-1-100002-22-200000000-1-111-1-11100000000000000000000000000000000
χ654444-244-4-4-244-2-24444-2-24-2-2-2-2444-2-22-4-4-4-4-4-4-4-42000000000000-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ664444-24-244-24-2-2-24-24-2-21-2-21-21-2-2-2-21-24-24-2-2-2-2-2-20000000000001111-21-211111004400000000-2-2-2-20000000000-2-20000111100000000000000000000
χ674444-24-244-24-2-2-24-24-2-21-2-21-21-2-2-2-21-24-24-2-2-2-2-2-20000000000001111-21-21111100-4-40000000022220000000000220000-1-1-1-100000000000000000000
χ684444-24-2-4-4-24-2-2-24-24-2-21-2-21-21-2-2-2-212-42-422222200000000000011112-12-1-1-1-1-1000000000000−2i32i3−2i32i30000000000000000i3−i3i3−i300000000000000000000
χ694444-24-2-4-4-24-2-2-24-24-2-21-2-21-21-2-2-2-212-42-422222200000000000011112-12-1-1-1-1-10000000000002i3−2i32i3−2i30000000000000000−i3i3−i3i300000000000000000000
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χ954-44-4-244002-442-24-4-4-4-2-242-222-4-44-220000000000000000000000-22-220000000000000000000000000000000000000000000000000000000000−666−600
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χ1074-4-44-2-24-44-22-4222-4-241-2-2-121-2-222-12-22-4-2422-2-220000000000001-1-11-121-2-1-1110000000023−23−23230000000000000000−333−3000000000000000000000000
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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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χ11388-8-8-4-4-4004-44-444-4442222-2-2-2-22-2-22000006i−6i6i−6i0000000000000-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ11488-8-8-4-4-4004-44-444-4442222-2-2-2-22-2-2200000−6i6i−6i6i0000000000000-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1158-88-8-48-4004-8-44-484-84-42-4424-244-4-4-200000000000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000
χ1168-88-8-4-48004484-4-4-84-82-4-4-2-4-2444-42400000000000000000000002-22-20000000000000000000000000000000000000000000000000000000000000000
χ1178-88-8-4-4-40044-44-4-4444222-22-2-2-2-222-2000006i−6i−6i6i0000000000000-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
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Here i is the imaginary unit (i² = −1).