Finite Group Databasebeta

← Group #13155721

Character table — Group #13155721

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order122233344666666666121212123336666666661212121212121212121212124444121212123666121212121212448812121212121212121212121212121212121224242424242424242424242424242424121212121212224466668824242424121222
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111
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
χ911-1-11111-1111-1-1-1-1-1-111-1-1111-1-1-1111-1-1-11-1-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-1i−i1-1iii−i−i−iii−i−iiiii−i−i−i−i11-1-1111111-1-1-1-1-1-1i−iii−i−i1-1i−i11-1-1i−iii−i−ii−i1-1
χ1011-1-11111-1111-1-1-1-1-1-111-1-1111-1-1-1111-1-1-11-1-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-1i−i-11iii−i−i−iii−i−iiiii−i−i−i−i-1-111-1-1-1-1-1-1111111i−iii−i−i1-1−ii11-1-1−ii−i−iii−ii-11
χ1111-1-11111-1111-1-1-1-1-1-111-1-1111-1-1-1111-1-1-11-1-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-1−ii1-1iii−i−i−i−i−iiiiiii−i−i−i−i11-1-1111111-1-1-1-1-1-1−ii−i−iii-11−ii-1-111i−iii−i−i−ii-11
χ1211-1-11111-1111-1-1-1-1-1-111-1-1111-1-1-1111-1-1-11-1-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-1−ii-11iii−i−i−i−i−iiiiiii−i−i−i−i-1-111-1-1-1-1-1-1111111−ii−i−iii-11i−i-1-111−ii−i−iiii−i1-1
χ1311-1-11111-1111-1-1-1-1-1-111-1-1111-1-1-1111-1-1-11-1-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-1i−i1-1−i−i−iiiiii−i−i−i−i−i−iiiii11-1-1111111-1-1-1-1-1-1i−iii−i−i-11i−i-1-111−ii−i−iiii−i-11
χ1411-1-11111-1111-1-1-1-1-1-111-1-1111-1-1-1111-1-1-11-1-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-1i−i-11−i−i−iiiiii−i−i−i−i−i−iiiii-1-111-1-1-1-1-1-1111111i−iii−i−i-11−ii-1-111i−iii−i−i−ii1-1
χ1511-1-11111-1111-1-1-1-1-1-111-1-1111-1-1-1111-1-1-11-1-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-1−ii1-1−i−i−iiii−i−iii−i−i−i−iiiii11-1-1111111-1-1-1-1-1-1−ii−i−iii1-1−ii11-1-1−ii−i−iii−ii1-1
χ1611-1-11111-1111-1-1-1-1-1-111-1-1111-1-1-1111-1-1-11-1-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-1−ii-11−i−i−iiii−i−iii−i−i−i−iiiii-1-111-1-1-1-1-1-1111111−ii−i−iii1-1i−i11-1-1i−iii−i−ii−i-11
χ172222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222222222-2-2-2-2-2-200002-2-22-2-2000022-2-222-2-20000000000000000000000000000000000000000
χ182222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2-2-20000-222-2220000-2-222-2-2220000000000000000000000000000000000000000
χ19222222-12222-122-12-1222222-1-122-12-1-1-1-1-1-12-1-1-122-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1220022-122-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-12200-1-1-1-10000000000
χ20222222-12222-122-12-1222222-1-122-12-1-1-1-1-1-12-1-1-122-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20022-122-11111-1-1-1-1-1-1-1-10000000000000000-2-21111-2-20011110000000000
χ21222222-12222-122-12-1222222-1-122-12-1-1-1-1-1-12-1-1-122-1-1222-2-2-2-21111-1-1-1-1-1-1-1-1-1-12200-2-21-2-21-1-1-1-111111111000000000000000022-1-1-1-1-2-20011110000000000
χ22222222-12222-122-12-1222222-1-122-12-1-1-1-1-1-12-1-1-122-1-1222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-2-200-2-21-2-211111111111110000000000000000-2-211112200-1-1-1-10000000000
χ23222222-1-2-222-122-12-12-2-2-2-22-1-122-12-1-1-1-1-11-2111-2-211-2-2-222-2-2-1-1-1-1-1-1-1-111111100002-212-21−i3i3−i3i3-1-111-1-111000000000000000000−i3i3−i3i30000−i3i3−i3i30000000000
χ24222222-1-2-222-122-12-12-2-2-2-22-1-122-12-1-1-1-1-11-2111-2-211-2-2-222-2-2-1-1-1-1-1-1-1-111111100002-212-21i3−i3i3−i3-1-111-1-111000000000000000000i3−i3i3−i30000i3−i3i3−i30000000000
χ25222222-1-2-222-122-12-12-2-2-2-22-1-122-12-1-1-1-1-11-2111-2-211-2-2-2-2-2221111-1-1-1-11111110000-22-1-22-1−i3i3−i3i311-1-111-1-1000000000000000000−i3i3−i3i30000i3−i3i3−i30000000000
χ26222222-1-2-222-122-12-12-2-2-2-22-1-122-12-1-1-1-1-11-2111-2-211-2-2-2-2-2221111-1-1-1-11111110000-22-1-22-1i3−i3i3−i311-1-111-1-1000000000000000000i3−i3i3−i30000−i3i3−i3i30000000000
χ2722222-12222-12222-12-12222-12-1-1-1-1-12-122-12-1222-1-122-1-1-100000000-1-1-1-1-1-1-1-1-1-122220000002222000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100220000000000-1-100
χ2822222-12222-12222-12-12222-12-1-1-1-1-12-122-12-1222-1-122-1-1-100000000-1-1-1-1-1-1-1-1-1-122-2-2000000222200000000-2-2-2-2111111111111-1-1-1-1-1-100-2-200000000001100
χ2922222-12222-12222-12-12222-12-1-1-1-1-12-122-12-1222-1-122-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-222000000-2-2-2-2000000002222-1-1-1-1-1-1-1-1-1-1-1-111111100-2-200000000001100
χ3022222-12222-12222-12-12222-12-1-1-1-1-12-122-12-1222-1-122-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000-2-2-2-200000000-2-2-2-211111111111111111100220000000000-1-100
χ312222-12222-122-1-12222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-122222222-1-1-1-122-1-1-1-10022-1-12-1-120000-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000000000000022-1-1-1-10000
χ322222-12222-122-1-12222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-122222222-1-1-1-122-1-1-1-100-2-2-1-12-1-120000-1-1-1-1-1-1-1-11111-2-21111-2-2111100000000000000-2-211110000
χ332222-12222-122-1-12222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-1002211-211-2000011111111-1-1-1-122-1-1-1-122-1-1-1-100000000000000-2-211110000
χ342222-12222-122-1-12222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-100-2-211-211-20000111111111111-2-21111-2-211110000000000000022-1-1-1-10000
χ352222-122-2-2-122-1-122221111-1-12-1-12-1-12-1-12-2-2-2111111-21122-2-22222-1-1-1-1-2-211110000-11-2-11-20000-1-111-1-1113−33−30033−3−30033−3−300000000000000003−33−30000
χ362222-122-2-2-122-1-122221111-1-12-1-12-1-12-1-12-2-2-2111111-21122-2-22222-1-1-1-1-2-211110000-11-2-11-20000-1-111-1-111−33−3300−3−33300−3−3330000000000000000−33−330000
χ372222-122-2-2-122-1-122221111-1-12-1-12-1-12-1-12-2-2-2111111-211-2-222-2-2-2-2-1-1-1-1-2-2111100001-121-12000011-1-111-1-13−33−30033−3−30033−3−30000000000000000−33−330000
χ382222-122-2-2-122-1-122221111-1-12-1-12-1-12-1-12-2-2-2111111-211-2-222-2-2-2-2-1-1-1-1-2-2111100001-121-12000011-1-111-1-1−33−3300−3−33300−3−33300000000000000003−33−30000
χ3922-2-2222-22222-2-2-2-2-2-2-2-222222-2-2-2222-2-2-2-222-2-22222-2-2-22i−2i−2i2i2i2i−2i−2i2-2-22-22-2-22200002i−2i−2i−2i2i2i00002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ4022-2-2222-22222-2-2-2-2-2-2-2-222222-2-2-2222-2-2-2-222-2-22222-2-2-2−2i2i2i−2i−2i−2i2i2i2-2-22-22-2-2220000−2i2i2i2i−2i−2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ4122-2-222-12-222-1-2-21-21-222-2-22-1-1-2-212-1-1111-1-21-1-1-2-2112222i−2i2i−2i−i−iii-111-1-11-1-1112i−2i002i2i−i−2i−2ii−i−iii−i−i−i−iiiii00000000000000002i−2i−i−iii2-200-1-1110000000000
χ4222-2-222-12-222-1-2-21-21-222-2-22-1-1-2-212-1-1111-1-21-1-1-2-2112222i−2i2i−2i−i−iii-111-1-11-1-111−2i2i002i2i−i−2i−2iiii−i−i−i−i−i−iiiii0000000000000000−2i2iii−i−i-220011-1-10000000000
χ4322-2-222-12-222-1-2-21-21-222-2-22-1-1-2-212-1-1111-1-21-1-1-2-211222−2i2i−2i2iii−i−i-111-1-11-1-1112i−2i00−2i−2ii2i2i−i−i−iiiiiii−i−i−i−i00000000000000002i−2i−i−iii-220011-1-10000000000
χ4422-2-222-12-222-1-2-21-21-222-2-22-1-1-2-212-1-1111-1-21-1-1-2-211222−2i2i−2i2iii−i−i-111-1-11-1-111−2i2i00−2i−2ii2i2i−iii−i−iiiii−i−i−i−i0000000000000000−2i2iii−i−i2-200-1-1110000000000
χ4522-2-222-1-2222-1-2-21-21-2-2-2222-1-1-2-212-1-111112-11122-1-1-2-2-22i−2i−2i2i−i−iii-111-11-111-1-100002i−2ii−2i2i−i3−3−33−i−iiiii−i−i0000000000000000003−3−330000−i3i3i3−i30000000000
χ4622-2-222-1-2222-1-2-21-21-2-2-2222-1-1-2-212-1-111112-11122-1-1-2-2-22i−2i−2i2i−i−iii-111-11-111-1-100002i−2ii−2i2i−i−333−3−i−iiiii−i−i000000000000000000−333−30000i3−i3−i3i30000000000
χ4722-2-222-1-2222-1-2-21-21-2-2-2222-1-1-2-212-1-111112-11122-1-1-2-2-2−2i2i2i−2iii−i−i-111-11-111-1-10000−2i2i−i2i−2ii3−3−33ii−i−i−i−iii0000000000000000003−3−330000i3−i3−i3i30000000000
χ4822-2-222-1-2222-1-2-21-21-2-2-2222-1-1-2-212-1-111112-11122-1-1-2-2-2−2i2i2i−2iii−i−i-111-11-111-1-10000−2i2i−i2i−2ii−333−3ii−i−i−i−iii000000000000000000−333−30000−i3i3i3−i30000000000
χ4922-2-22-122-22-12-2-2-21-2122-2-2-12-1111-12-1-2-2121-22211-2-2-1-1-100000000-111-1-11-1-1112i−2i2-20000002i2i−2i−2i0000000022-2-2-1-1-1-1-1-1111111−ii−i−iii002i−2i0000000000−ii00
χ5022-2-22-122-22-12-2-2-21-2122-2-2-12-1111-12-1-2-2121-22211-2-2-1-1-100000000-111-1-11-1-1112i−2i-220000002i2i−2i−2i00000000-2-222111111-1-1-1-1-1-1−ii−i−iii00−2i2i0000000000i−i00
χ5122-2-22-122-22-12-2-2-21-2122-2-2-12-1111-12-1-2-2121-22211-2-2-1-1-100000000-111-1-11-1-111−2i2i2-2000000−2i−2i2i2i0000000022-2-2-1-1-1-1-1-1111111i−iii−i−i00−2i2i0000000000i−i00
χ5222-2-22-122-22-12-2-2-21-2122-2-2-12-1111-12-1-2-2121-22211-2-2-1-1-100000000-111-1-11-1-111−2i2i-22000000−2i−2i2i2i00000000-2-222111111-1-1-1-1-1-1i−iii−i−i002i−2i0000000000−ii00
χ5322-2-2-1222-2-12211-2-2-2-2-1-111-1-1211-2-1-1211-22-2-2-1-111112-1-12i−2i2i−2i2i2i−2i−2i-111-12-2-1-111002-2−i−i2iii−2i0000−i−i−i−iiiii-1-11122-1-1-1-1-2-21111000000000000002i−2i−i−iii0000
χ5422-2-2-1222-2-12211-2-2-2-2-1-111-1-1211-2-1-1211-22-2-2-1-111112-1-12i−2i2i−2i2i2i−2i−2i-111-12-2-1-11100-22−i−i2iii−2i0000−i−i−i−iiiii11-1-1-2-2111122-1-1-1-100000000000000−2i2iii−i−i0000
χ5522-2-2-1222-2-12211-2-2-2-2-1-111-1-1211-2-1-1211-22-2-2-1-111112-1-1−2i2i−2i2i−2i−2i2i2i-111-12-2-1-111002-2ii−2i−i−i2i0000iiii−i−i−i−i-1-11122-1-1-1-1-2-2111100000000000000−2i2iii−i−i0000
χ5622-2-2-1222-2-12211-2-2-2-2-1-111-1-1211-2-1-1211-22-2-2-1-111112-1-1−2i2i−2i2i−2i−2i2i2i-111-12-2-1-11100-22ii−2i−i−i2i0000iiii−i−i−i−i11-1-1-2-2111122-1-1-1-1000000000000002i−2i−i−iii0000
χ5722-2-2-122-22-12211-2-2-2-211-1-1-1-1211-2-1-1211-2-22211-1-1-1-1-2112i−2i−2i2i2i2i−2i−2i-111-1-2211-1-10000−ii−2ii−i2i0000−i−iiiii−i−i3−3−330033−3−300−3−3330000000000000000i3−i3−i3i30000
χ5822-2-2-122-22-12211-2-2-2-211-1-1-1-1211-2-1-1211-2-22211-1-1-1-1-2112i−2i−2i2i2i2i−2i−2i-111-1-2211-1-10000−ii−2ii−i2i0000−i−iiiii−i−i−333−300−3−3330033−3−30000000000000000−i3i3i3−i30000
χ5922-2-2-122-22-12211-2-2-2-211-1-1-1-1211-2-1-1211-2-22211-1-1-1-1-211−2i2i2i−2i−2i−2i2i2i-111-1-2211-1-10000i−i2i−ii−2i0000ii−i−i−i−iii3−3−330033−3−300−3−3330000000000000000−i3i3i3−i30000
χ6022-2-2-122-22-12211-2-2-2-211-1-1-1-1211-2-1-1211-2-22211-1-1-1-1-211−2i2i2i−2i−2i−2i2i2i-111-1-2211-1-10000i−i2i−ii−2i0000ii−i−i−i−iii−333−300−3−3330033−3−30000000000000000i3−i3−i3i30000
χ6144444-24-4-44-24444-24-2-4-4-4-4-24-2-2-2-2-24-244-2-42-4-4-422-4-422200000000-2-2-2-222222200000000000000000000000000000000000000000000000000000000000000
χ6244444-2-2444-2-244-2-2-2-24444-2-21-2-21-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-20000000011111111114400000000-2-2-2-2000000000000000000000000-2-21111000000000000000000
χ6344444-2-2444-2-244-2-2-2-24444-2-21-2-21-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-2000000001111111111-4-400000000222200000000000000000000000022-1-1-1-1000000000000000000
χ6444444-2-2-4-44-2-244-2-2-2-2-4-4-4-4-2-21-2-21-2-21-2-21222222222222000000001111-1-1-1-1-1-10000000000−2i32i3−2i32i300000000000000000000000000i3−i3i3−i3000000000000000000
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χ664444-24-244-24-2-2-2-24-24-2-2-2-2-21-2-2-2-2-21-211-2-24-211-2-2114-2-24444-2-2-2-21111-2-211110000-2-2-2-2-2-20000111111110000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.