Finite Group Databasebeta

← Group #13155751

Character table — Group #13155751

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111222222222222224444444444444444444444666666666666888888888888121212121212121212121212121212121212121212121212242424242424242424242424363636363636363636363636363636363636108108
order12442333466612121212121233366666666121212121212121212121288882424242424242424366666121212121212888824242424242424242424242424242424242424242424242424242424242424242244666688121212122424242444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-11111111111-1-11111-1-1-1-11-11-111-1-1-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-1111111111111-1-111-1-1-1-11111-11-11-1-111-1-1-1-111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-11-1-111-1-1-1-111-1-1-1-111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-11-111-1-1-1-111-1-1-1-1-1-111
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
χ911-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11ii−i−iiiii−i−i−i−i1-1-1-1-111111-1-1i−ii−iii−i−iii−i−iii−i−iiiii−i−i−i−ii−ii−iii−i−iii−i−i11-1-111111-1-1-1-1-111-1-1i−i
χ1011-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11ii−i−iiiii−i−i−i−i1-1-1-1-111111-1-1i−i−iiii−i−iii−i−i−i−iiiiiii−i−i−i−ii−i−iiii−i−i−i−iii1-1-1111-1-1-11-1-111-1-111−ii
χ1111-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11ii−i−iiiii−i−i−i−i1-1-1-1-111111-1-1−iii−iii−i−i−i−iiiii−i−iiiii−i−i−i−i−iii−i−i−iiiii−i−i-111-1-1-111-1111-1-1-1-111−ii
χ1211-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11ii−i−iiiii−i−i−i−i1-1-1-1-111111-1-1−ii−iiii−i−i−i−iii−i−iiiiiii−i−i−i−i−ii−ii−i−iii−i−iii-1-111-1-1-1-11-1111111-1-1i−i
χ1311-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11−i−iii−i−i−i−iiiii1-1-1-1-111111-1-1i−ii−i−i−iiiii−i−iii−i−i−i−i−i−iiiiii−ii−iii−i−iii−i−i-1-111-1-1-1-11-1111111-1-1−ii
χ1411-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11−i−iii−i−i−i−iiiii1-1-1-1-111111-1-1i−i−ii−i−iiiii−i−i−i−iii−i−i−i−iiiiii−i−iiii−i−i−i−iii-111-1-1-111-1111-1-1-1-111i−i
χ1511-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11−i−iii−i−i−i−iiiii1-1-1-1-111111-1-1−iii−i−i−iii−i−iiiii−i−i−i−i−i−iiiii−iii−i−i−iiiii−i−i1-1-1111-1-1-11-1-111-1-111i−i
χ1611-1-1-11111111-1-1-1-1-1-1111-1-1-1-1-11111111-1-1-1-1-1-11−i−iii−i−i−i−iiiii1-1-1-1-111111-1-1−ii−ii−i−iii−i−iii−i−iii−i−i−i−iiiii−ii−ii−i−iii−i−iii11-1-111111-1-1-1-1-111-1-1−ii
χ172222222-1222-12222-1-12-1-122-1-1-12-1-12-1-1-122-1-1-1-12222222-1-122-1-1-12-1-1-1-12-1-1-1-1-100222-12-10000-1-1-1-1-1-1-1-1-1-1-1-100220000-1-1-1-1020200-1-10000-1-1000000
χ182222222-1222-12222-1-12-1-122-1-1-12-1-12-1-1-122-1-1-1-12222222-1-122-1-1-12-1-1-1-12-1-1-1-1-100-2-22-12-100001111-1-1-1-1-1-1-1-100-2-2000011110-20-20011000011000000
χ192222222-1222-12222-1-12-1-122-1-1-12-1-12-1-1-122-1-1-1-12-2-2-2-2-2-211-2-211-12-1-1-1-12-1-1-1-1-10022-21-210000-1-1-1-11111111100220000-1-1-1-10-20-20011000011000000
χ202222222-1222-12222-1-12-1-122-1-1-12-1-12-1-1-122-1-1-1-12-2-2-2-2-2-211-2-211-12-1-1-1-12-1-1-1-1-100-2-2-21-21000011111111111100-2-200001111020200-1-10000-1-1000000
χ21222222-1222-1222-1-122-12-12-12-1-1-12-1-12-1-1-1-122-1-122222-1-122-1-122-1-12-1-1-1-12-1-1-1-12200-12-12-1-1-1-10000-1-1-1-1-1-1-1-12200-1-1-1-100002020-1-10000-1-100000000
χ22222222-1222-1222-1-122-12-12-12-1-1-12-1-12-1-1-1-122-1-122222-1-122-1-122-1-12-1-1-1-12-1-1-1-1-2-200-12-1211110000-1-1-1-1-1-1-1-1-2-20011110000-20-201100001100000000
χ23222222-1222-1222-1-122-12-12-12-1-1-12-1-12-1-1-1-122-1-12-2-2-2-211-2-211-2-2-1-12-1-1-1-12-1-1-1-122001-21-2-1-1-1-10000111111112200-1-1-1-10000-20-201100001100000000
χ24222222-1222-1222-1-122-12-12-12-1-1-12-1-12-1-1-1-122-1-12-2-2-2-211-2-211-2-2-1-12-1-1-1-12-1-1-1-1-2-2001-21-21111000011111111-2-200111100002020-1-10000-1-100000000
χ2522222-1222-122-1-12222-1-12-12222-1-122222-1-1-1-122-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1222200002222222200000000-1-1-1-1-1-1-1-1-1-1-1-100000000220000-1-1-1-100
χ2622222-1222-122-1-12222-1-12-12222-1-122222-1-1-1-122-1000000000000-1-1-1-1-1-1-1-1-1-1-1-122-2-200002222-2-2-2-200000000-1-111-1-1-1-1111100000000-2-20000111100
χ2722222-1222-122-1-12222-1-12-12222-1-122222-1-1-1-122-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2220000-2-2-2-222220000000011-1-11111-1-1-1-100000000-2-20000111100
χ2822222-1222-122-1-12222-1-12-12222-1-122222-1-1-1-122-1000000000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-2-2-2-2-20000000011111111111100000000220000-1-1-1-100
χ292222-2222-2222222222222-2-2-2-2-2222-2-2-2-2222222-22-22-222-2-222-2-22-2-2-2-22-2-2-2-2220000-22-220000000022-2-222-2-200000000000000000000000000000000
χ302222-2222-2222222222222-2-2-2-2-2222-2-2-2-2222222-2-22-22-2-222-2-2222-2-2-2-22-2-2-2-22200002-22-200000000-2-222-2-22200000000000000000000000000000000
χ312222-222-1-222-12222-1-12-1-1-2-21112-1-1-211122-1-1-1-1-22-22-222112211-1-2111-1-2111-1-10000-2-1-2-10000−i3i3−i3i3-1-111-1-11100000000−i3i3−i3i3000000−i3i30000−i3i3000000
χ322222-222-1-222-12222-1-12-1-1-2-21112-1-1-211122-1-1-1-1-22-22-222112211-1-2111-1-2111-1-10000-2-1-2-10000i3−i3i3−i3-1-111-1-11100000000i3−i3i3−i3000000i3−i30000i3−i3000000
χ332222-222-1-222-12222-1-12-1-1-2-21112-1-1-211122-1-1-1-1-2-22-22-2-2-1-1-2-2-1-1-1-2111-1-2111-1-1000021210000−i3i3−i3i311-1-111-1-100000000−i3i3−i3i3000000i3−i30000i3−i3000000
χ342222-222-1-222-12222-1-12-1-1-2-21112-1-1-211122-1-1-1-1-2-22-22-2-2-1-1-2-2-1-1-1-2111-1-2111-1-1000021210000i3−i3i3−i311-1-111-1-100000000i3−i3i3−i3000000−i3i30000−i3i3000000
χ352222-22-12-22-1222-1-122-12-1-21-211-12-11-211-1-122-1-1-22-22-2-1-1-2-2-1-1-2-2-11-211-11-211-1-100001212−i3i3−i3i30000-1-111-1-1110000−i3i3−i3i300000000−i3i30000−i3i300000000
χ362222-22-12-22-1222-1-122-12-1-21-211-12-11-211-1-122-1-1-22-22-2-1-1-2-2-1-1-2-2-11-211-11-211-1-100001212i3−i3i3−i30000-1-111-1-1110000i3−i3i3−i300000000i3−i30000i3−i300000000
χ372222-22-12-22-1222-1-122-12-1-21-211-12-11-211-1-122-1-1-2-22-2211221122-11-211-11-211-1-10000-1-2-1-2−i3i3−i3i3000011-1-111-1-10000−i3i3−i3i300000000i3−i30000i3−i300000000
χ382222-22-12-22-1222-1-122-12-1-21-211-12-11-211-1-122-1-1-2-22-2211221122-11-211-11-211-1-10000-1-2-1-2i3−i3i3−i3000011-1-111-1-10000i3−i3i3−i300000000−i3i30000−i3i300000000
χ3922-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-22i−2i−2i2i2i2i−2i−2i−2i−2i2i2i222222-2-2-2-2-2-20000−2i2i2i−2i000000002i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000
χ4022-2-22222-2222-2-2-2-2-2-222222222222-2-2-2-2-2-2-2-2-2-2-2−2i2i2i−2i−2i−2i2i2i2i2i−2i−2i222222-2-2-2-2-2-200002i−2i−2i2i00000000−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000
χ4122-2-2222-1-222-1-2-2-2-2112-1-122-1-1-12-1-1-2111-2-21111-22i−2i−2i2i2i2iii−2i−2i−i−i-12-1-1-1-1-2111110000−2i−i2ii00003−3−33−i−iiiii−i−i000000003−3−33000000−i3i30000i3−i3000000
χ4222-2-2222-1-222-1-2-2-2-2112-1-122-1-1-12-1-1-2111-2-21111-22i−2i−2i2i2i2iii−2i−2i−i−i-12-1-1-1-1-2111110000−2i−i2ii0000−333−3−i−iiiii−i−i00000000−333−3000000i3−i30000−i3i3000000
χ4322-2-2222-1-222-1-2-2-2-2112-1-122-1-1-12-1-1-2111-2-21111-2−2i2i2i−2i−2i−2i−i−i2i2iii-12-1-1-1-1-21111100002ii−2i−i00003−3−33ii−i−i−i−iii000000003−3−33000000i3−i30000−i3i3000000
χ4422-2-2222-1-222-1-2-2-2-2112-1-122-1-1-12-1-1-2111-2-21111-2−2i2i2i−2i−2i−2i−i−i2i2iii-12-1-1-1-1-21111100002ii−2i−i0000−333−3ii−i−i−i−iii00000000−333−3000000−i3i30000i3−i3000000
χ4522-2-222-12-22-12-2-211-2-2-12-12-12-1-1-12-11-21111-2-211-22i−2i−2i2i−i−i−2i−2iii2i2i-1-12-1-1-11-211110000i2i−i−2i3−3−330000−i−iiiii−i−i00003−3−3300000000−i3i30000i3−i300000000
χ4622-2-222-12-22-12-2-211-2-2-12-12-12-1-1-12-11-21111-2-211-22i−2i−2i2i−i−i−2i−2iii2i2i-1-12-1-1-11-211110000i2i−i−2i−333−30000−i−iiiii−i−i0000−333−300000000i3−i30000−i3i300000000
χ4722-2-222-12-22-12-2-211-2-2-12-12-12-1-1-12-11-21111-2-211-2−2i2i2i−2iii2i2i−i−i−2i−2i-1-12-1-1-11-211110000−i−2ii2i3−3−330000ii−i−i−i−iii00003−3−3300000000i3−i30000−i3i300000000
χ4822-2-222-12-22-12-2-211-2-2-12-12-12-1-1-12-11-21111-2-211-2−2i2i2i−2iii2i2i−i−i−2i−2i-1-12-1-1-11-211110000−i−2ii2i−333−30000ii−i−i−i−iii0000−333−300000000−i3i30000i3−i300000000
χ4922-2-2-222-1222-1-2-2-2-2112-1-1-2-21112-1-12-1-1-1-2-2111122i2i−2i−2i2i2i−i−i−2i−2iii-1-2111-12-1-1-111002i−2i2i−i−2ii0000−i−iii−i−i−i−iiiii002i−2i0000−i−iii020-200-1-1000011000000
χ5022-2-2-222-1222-1-2-2-2-2112-1-1-2-21112-1-12-1-1-1-2-2111122i2i−2i−2i2i2i−i−i−2i−2iii-1-2111-12-1-1-11100−2i2i2i−i−2ii0000ii−i−i−i−i−i−iiiii00−2i2i0000ii−i−i0-20200110000-1-1000000
χ5122-2-2-222-1222-1-2-2-2-2112-1-1-2-21112-1-12-1-1-1-2-211112−2i−2i2i2i−2i−2iii2i2i−i−i-1-2111-12-1-1-111002i−2i−2ii2i−i0000−i−iiiiiii−i−i−i−i002i−2i0000−i−iii0-20200110000-1-1000000
χ5222-2-2-222-1222-1-2-2-2-2112-1-1-2-21112-1-12-1-1-1-2-211112−2i−2i2i2i−2i−2iii2i2i−i−i-1-2111-12-1-1-11100−2i2i−2ii2i−i0000ii−i−iiiii−i−i−i−i00−2i2i0000ii−i−i020-200-1-1000011000000
χ5322-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-1-12-1-111-2-21122i2i−2i−2i−i−i2i2iii−2i−2i-11-211-1-12-1-1112i−2i00−i2ii−2i−i−iii0000−i−i−i−iiiii2i−2i00−i−iii000020-20-1-100001100000000
χ5422-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-1-12-1-111-2-21122i2i−2i−2i−i−i2i2iii−2i−2i-11-211-1-12-1-111−2i2i00−i2ii−2iii−i−i0000−i−i−i−iiiii−2i2i00ii−i−i0000-2020110000-1-100000000
χ5522-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-1-12-1-111-2-2112−2i−2i2i2iii−2i−2i−i−i2i2i-11-211-1-12-1-1112i−2i00i−2i−i2i−i−iii0000iiii−i−i−i−i2i−2i00−i−iii0000-2020110000-1-100000000
χ5622-2-2-22-1222-12-2-211-2-2-12-1-21-211-12-1-12-1-111-2-2112−2i−2i2i2iii−2i−2i−i−i2i2i-11-211-1-12-1-111−2i2i00i−2i−i2iii−i−i0000iiii−i−i−i−i−2i2i00ii−i−i000020-20-1-100001100000000
χ5722-2-2-2-1222-12211-2-2-2-2-1-121-2-2-2-2-1-1222221111-2-2-1000000000000-11111-1-1-1-1-1112i−2i2i−2i00002i2i−2i−2i2i2i−2i−2i00000000−ii−ii−i−iii−i−iii000000002-20000-1-11100
χ5822-2-2-2-1222-12211-2-2-2-2-1-121-2-2-2-2-1-1222221111-2-2-1000000000000-11111-1-1-1-1-1112i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i00000000−iii−i−i−iiiii−i−i00000000-22000011-1-100
χ5922-2-2-2-1222-12211-2-2-2-2-1-121-2-2-2-2-1-1222221111-2-2-1000000000000-11111-1-1-1-1-111−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i00000000i−i−iiii−i−i−i−iii00000000-22000011-1-100
χ6022-2-2-2-1222-12211-2-2-2-2-1-121-2-2-2-2-1-1222221111-2-2-1000000000000-11111-1-1-1-1-111−2i2i−2i2i0000−2i−2i2i2i−2i−2i2i2i00000000i−ii−iii−i−iii−i−i000000002-20000-1-11100
χ61444444-2-244-2-244-2-2-2-2-2-214-2-211-2-21-2-211-2-2-2-21144444-2-2-2-2-2-2-2-21-2-2111-2-211110000-2-2-2-2000000001111111100000000000000000000000000000000
χ62444444-2-244-2-244-2-2-2-2-2-214-2-211-2-21-2-211-2-2-2-2114-4-4-4-4222222221-2-2111-2-211110000222200000000-1-1-1-1-1-1-1-100000000000000000000000000000000
χ6344444-24-24-24-2-2-244-2-2-21-2-24-2-2-2-21-24-2-2-2-2-211-2-2-20000000000001-21111-211111004400000000-2-2-2-20000000000-2-20000111100000000000000000000
χ6444444-24-24-24-2-2-244-2-2-21-2-24-2-2-2-21-24-2-2-2-2-211-2-2-20000000000001-21111-21111100-4-40000000022220000000000220000-1-1-1-100000000000000000000
χ6544444-2-244-2-24-2-2-2-2441-2-2-2-24-2-21-2-2-24-2-211-2-2-2-2-200000000000011-21111-2111144000000-2-2-2-2000000000000-2-2001111000000000000000000000000
χ6644444-2-244-2-24-2-2-2-2441-2-2-2-24-2-21-2-2-24-2-211-2-2-2-2-200000000000011-21111-21111-4-400000022220000000000002200-1-1-1-1000000000000000000000000
χ674444-44-2-2-44-2-244-2-2-2-2-2-21-422-1-1-2-2122-1-1-2-2-2-211-44-44-4-2-222-2-222122-1-1122-1-11100002-22-20000000011-1-111-1-100000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.