Finite Group Databasebeta

← Group #13155671

Character table — Group #13155671

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order122233344666666666121212123336666666661212121212121212121212124444121212123666121212121212226666881212121212121212121212121212242424242424242424242424242424246666664444881212121224242424121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111
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
χ91-11-11111-1-1-111-1-1-11-111-1-1111-1-1-1-1111-1-11-1-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-11-111-1-11-1iii−i−i−iiiii−i−i−i−i11-1-1111111-1-1-1-1-1-11-111-1-11-1i−ii−iii−i−iii−i−i1-1i−i
χ101-11-11111-1-1-111-1-1-11-111-1-1111-1-1-1-1111-1-11-1-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-11-111-1-1-11iii−i−i−iiiii−i−i−i−i-1-111-1-1-1-1-1-11111111-111-1-1-11i−i−iiii−i−i−i−iii-11−ii
χ111-11-11111-1-1-111-1-1-11-111-1-1111-1-1-1-1111-1-11-1-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-1-11-1-1111-1iii−i−i−iiiii−i−i−i−i11-1-1111111-1-1-1-1-1-1-11-1-111-11−iii−i−i−iiiii−i−i-11−ii
χ121-11-11111-1-1-111-1-1-11-111-1-1111-1-1-1-1111-1-11-1-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-1-11-1-111-11iii−i−i−iiiii−i−i−i−i-1-111-1-1-1-1-1-1111111-11-1-1111-1−ii−ii−i−iii−i−iii1-1i−i
χ131-11-11111-1-1-111-1-1-11-111-1-1111-1-1-1-1111-1-11-1-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-11-111-1-11-1−i−i−iiii−i−i−i−iiiii11-1-1111111-1-1-1-1-1-11-111-1-11-1−ii−ii−i−iii−i−iii1-1−ii
χ141-11-11111-1-1-111-1-1-11-111-1-1111-1-1-1-1111-1-11-1-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-11-111-1-1-11−i−i−iiii−i−i−i−iiiii-1-111-1-1-1-1-1-11111111-111-1-1-11−iii−i−i−iiiii−i−i-11i−i
χ151-11-11111-1-1-111-1-1-11-111-1-1111-1-1-1-1111-1-11-1-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-1-11-1-1111-1−i−i−iiii−i−i−i−iiiii11-1-1111111-1-1-1-1-1-1-11-1-111-11i−i−iiii−i−i−i−iii-11i−i
χ161-11-11111-1-1-111-1-1-11-111-1-1111-1-1-1-1111-1-11-1-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-1-11-1-111-11−i−i−iiii−i−i−i−iiiii-1-111-1-1-1-1-1-1111111-11-1-1111-1i−ii−iii−i−iii−i−i1-1−ii
χ172222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-2-2-20000000022-222-222-2-222-2-20000000000000000000000000000000000000000
χ182222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-200000000-2-22-2-22-2-222-2-2220000000000000000000000000000000000000000
χ19222222-122222-122-12-122222-1-122-1-12-1-1-1-1-1-12-1-122-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1002-122-12-1-1-1-1-1-1-1-1000000000000000022-1-1-1-1002200-1-1-1-100000000
χ20222222-122222-122-12-122222-1-122-1-12-1-1-1-1-1-12-1-122-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-21111002-122-12-1-1-1-1-1-1-1-10000000000000000-2-2111100-2-200111100000000
χ21222222-122222-122-12-122222-1-122-1-12-1-1-1-1-1-12-1-122-1-1222-2-2-2-21111-1-1-1-1-1-1-1-1-1-122-1-1-1-100-21-2-21-211111111000000000000000022-1-1-1-100-2-200111100000000
χ22222222-122222-122-12-122222-1-122-1-12-1-1-1-1-1-12-1-122-1-1222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-2-2111100-21-2-21-2111111110000000000000000-2-21111002200-1-1-1-100000000
χ23222222-1-2-2222-122-12-1-2-2-2-22-1-122-1-12-1-1-1-111-211-2-211-2-2-222-2-21111-1-1-1-111111100−i3i3−i3i3002-1-22-1-2-1-111-1-111000000000000000000−i3i3−i3i3000000−i3i3−i3i300000000
χ24222222-1-2-2222-122-12-1-2-2-2-22-1-122-1-12-1-1-1-111-211-2-211-2-2-222-2-21111-1-1-1-111111100i3−i3i3−i3002-1-22-1-2-1-111-1-111000000000000000000i3−i3i3−i3000000i3−i3i3−i300000000
χ25222222-1-2-2222-122-12-1-2-2-2-22-1-122-1-12-1-1-1-111-211-2-211-2-2-2-2-222-1-1-1-1-1-1-1-111111100−i3i3−i3i300-212-21211-1-111-1-1000000000000000000−i3i3−i3i3000000i3−i3i3−i300000000
χ26222222-1-2-2222-122-12-1-2-2-2-22-1-122-1-12-1-1-1-111-211-2-211-2-2-2-2-222-1-1-1-1-1-1-1-111111100i3−i3i3−i300-212-21211-1-111-1-1000000000000000000i3−i3i3−i3000000−i3i3−i3i300000000
χ2722222-1222-1-122222-122222-12-1-1-1-1-1-12-12222-122-1-122-1-1-100000000-1-1-1-1-1-1-1-1-1-122222222000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122000000000000-1-100
χ2822222-1222-1-122222-122222-12-1-1-1-1-1-12-12222-122-1-122-1-1-100000000-1-1-1-1-1-1-1-1-1-1222222-2-200000000000000-2-2-2-2111111111111-1-1-1-1-1-1-2-20000000000001100
χ2922222-1222-1-122222-122222-12-1-1-1-1-1-12-12222-122-1-122-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-222000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1111111-2-20000000000001100
χ3022222-1222-1-122222-122222-12-1-1-1-1-1-12-12222-122-1-122-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-200000000000000-2-2-2-211111111111111111122000000000000-1-100
χ312222-1222222-12-1-1222-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-122222222-1-1-1-122-1-1-1-100000022-12-1-12-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000000000220000-1-1-1-10000
χ322222-1222222-12-1-1222-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-122222222-1-1-1-122-1-1-1-1000000-2-2-12-1-12-1-1-1-1-1-1-1-1-11111-2-21111-2-211110000000000-2-2000011110000
χ332222-1222222-12-1-1222-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-1000000221-211-2111111111-1-1-1-122-1-1-1-122-1-1-1-10000000000-2-2000011110000
χ342222-1222222-12-1-1222-1-1-1-1-1-12-1-122-1-12-1-1222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-1000000-2-21-211-21111111111111-2-21111-2-211110000000000220000-1-1-1-10000
χ352222-122-2-222-12-1-12221111-1-12-1-122-1-12-1-1-2-2-2111111-21122-2-2-2-2-2-2-1-1-1-1-2-2111100000000-121-121-1-111-1-1113−33−30033−3−30033−3−300000000000000003−33−30000
χ362222-122-2-222-12-1-12221111-1-12-1-122-1-12-1-1-2-2-2111111-21122-2-2-2-2-2-2-1-1-1-1-2-2111100000000-121-121-1-111-1-111−33−3300−3−33300−3−3330000000000000000−33−330000
χ372222-122-2-222-12-1-12221111-1-12-1-122-1-12-1-1-2-2-2111111-211-2-2222222-1-1-1-1-2-21111000000001-2-11-2-111-1-111-1-13−33−30033−3−30033−3−30000000000000000−33−330000
χ382222-122-2-222-12-1-12221111-1-12-1-122-1-12-1-1-2-2-2111111-211-2-2222222-1-1-1-1-2-21111000000001-2-11-2-111-1-111-1-1−33−3300−3−33300−3−33300000000000000003−33−30000
χ392-22-2222-22-2-222-2-2-22-2-2-222222-2-2-2-2222-2-2-222-2-22222-2-2-22i−2i−2i2i−2i−2i2i2i2-2-22-22-2-222000000002i2i−2i−2i−2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ402-22-2222-22-2-222-2-2-22-2-2-222222-2-2-2-2222-2-2-222-2-22222-2-2-2−2i2i2i−2i2i2i−2i−2i2-2-22-22-2-22200000000−2i−2i2i2i2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ412-22-222-12-2-2-22-1-2-212122-2-22-1-1-2-2112-1-111-11-2-1-1-2-2112222i−2i2i−2i−i−iii-111-1-11-1-1112-2-1-111002i−i2i−2ii−2i−i−i−i−iiiii00000000000000002-2-1-111002i−2i00−i−iii00000000
χ422-22-222-12-2-2-22-1-2-212122-2-22-1-1-2-2112-1-111-11-2-1-1-2-2112222i−2i2i−2i−i−iii-111-1-11-1-111-2211-1-1002i−i2i−2ii−2i−i−i−i−iiiii0000000000000000-2211-1-100−2i2i00ii−i−i00000000
χ432-22-222-12-2-2-22-1-2-212122-2-22-1-1-2-2112-1-111-11-2-1-1-2-211222−2i2i−2i2iii−i−i-111-1-11-1-1112-2-1-11100−2ii−2i2i−i2iiiii−i−i−i−i00000000000000002-2-1-11100−2i2i00ii−i−i00000000
χ442-22-222-12-2-2-22-1-2-212122-2-22-1-1-2-2112-1-111-11-2-1-1-2-211222−2i2i−2i2iii−i−i-111-1-11-1-111-2211-1-100−2ii−2i2i−i2iiiii−i−i−i−i0000000000000000-2211-1-1002i−2i00−i−iii00000000
χ452-22-222-1-22-2-22-1-2-2121-2-2222-1-1-2-2112-1-1111-121122-1-1-2-2-22i−2i−2i2iii−i−i-111-11-111-1-100−i3i3i3−i3002i−i−2i−2ii2i−i−iiiii−i−i000000000000000000−i3i3i3−i30000003−3−3300000000
χ462-22-222-1-22-2-22-1-2-2121-2-2222-1-1-2-2112-1-1111-121122-1-1-2-2-22i−2i−2i2iii−i−i-111-11-111-1-100i3−i3−i3i3002i−i−2i−2ii2i−i−iiiii−i−i000000000000000000i3−i3−i3i3000000−333−300000000
χ472-22-222-1-22-2-22-1-2-2121-2-2222-1-1-2-2112-1-1111-121122-1-1-2-2-2−2i2i2i−2i−i−iii-111-11-111-1-100−i3i3i3−i300−2ii2i2i−i−2iii−i−i−i−iii000000000000000000−i3i3i3−i3000000−333−300000000
χ482-22-222-1-22-2-22-1-2-2121-2-2222-1-1-2-2112-1-1111-121122-1-1-2-2-2−2i2i2i−2i−i−iii-111-11-111-1-100i3−i3−i3i300−2ii2i2i−i−2iii−i−i−i−iii000000000000000000i3−i3−i3i30000003−3−3300000000
χ492-22-22-122-21122-2-2-2-1-222-2-2-12-11111-12-1-2-22-212211-2-2-1-1-100000000-111-1-11-1-1112-222-2-22-20000000000000022-2-2-1-1-1-1-1-1111111-11-1-1112-2000000000000-1100
χ502-22-22-122-21122-2-2-2-1-222-2-2-12-11111-12-1-2-22-212211-2-2-1-1-100000000-111-1-11-1-1112-222-2-2-2200000000000000-2-222111111-1-1-1-1-1-1-11-1-111-220000000000001-100
χ512-22-22-122-21122-2-2-2-1-222-2-2-12-11111-12-1-2-22-212211-2-2-1-1-100000000-111-1-11-1-111-22-2-2222-20000000000000022-2-2-1-1-1-1-1-11111111-111-1-1-220000000000001-100
χ522-22-22-122-21122-2-2-2-1-222-2-2-12-11111-12-1-2-22-212211-2-2-1-1-100000000-111-1-11-1-111-22-2-222-2200000000000000-2-222111111-1-1-1-1-1-11-111-1-12-2000000000000-1100
χ532-22-2-1222-2-2-2-1211-22-2-1-111-1-1211-2-2-1-12112-2-2-1-111112-1-12i−2i2i−2i2i2i−2i−2i-111-12-2-1-1110000002-2−i2i−ii−2ii−i−i−i−iiiii-1-11122-1-1-1-1-2-2111100000000002i−2i0000−i−iii0000
χ542-22-2-1222-2-2-2-1211-22-2-1-111-1-1211-2-2-1-12112-2-2-1-111112-1-12i−2i2i−2i2i2i−2i−2i-111-12-2-1-111000000-22−i2i−ii−2ii−i−i−i−iiiii11-1-1-2-2111122-1-1-1-10000000000−2i2i0000ii−i−i0000
χ552-22-2-1222-2-2-2-1211-22-2-1-111-1-1211-2-2-1-12112-2-2-1-111112-1-1−2i2i−2i2i−2i−2i2i2i-111-12-2-1-1110000002-2i−2ii−i2i−iiiii−i−i−i−i-1-11122-1-1-1-1-2-211110000000000−2i2i0000ii−i−i0000
χ562-22-2-1222-2-2-2-1211-22-2-1-111-1-1211-2-2-1-12112-2-2-1-111112-1-1−2i2i−2i2i−2i−2i2i2i-111-12-2-1-111000000-22i−2ii−i2i−iiiii−i−i−i−i11-1-1-2-2111122-1-1-1-100000000002i−2i0000−i−iii0000
χ572-22-2-122-22-2-2-1211-22-211-1-1-1-1211-2-2-1-1211-22211-1-1-1-1-2112i−2i−2i2i−2i−2i2i2i-111-1-2211-1-100000000−i2iii−2i−i−i−iiiii−i−i3−3−330033−3−300−3−3330000000000000000i3−i3−i3i30000
χ582-22-2-122-22-2-2-1211-22-211-1-1-1-1211-2-2-1-1211-22211-1-1-1-1-2112i−2i−2i2i−2i−2i2i2i-111-1-2211-1-100000000−i2iii−2i−i−i−iiiii−i−i−333−300−3−3330033−3−30000000000000000−i3i3i3−i30000
χ592-22-2-122-22-2-2-1211-22-211-1-1-1-1211-2-2-1-1211-22211-1-1-1-1-211−2i2i2i−2i2i2i−2i−2i-111-1-2211-1-100000000i−2i−i−i2iiii−i−i−i−iii3−3−330033−3−300−3−3330000000000000000−i3i3i3−i30000
χ602-22-2-122-22-2-2-1211-22-211-1-1-1-1211-2-2-1-1211-22211-1-1-1-1-211−2i2i2i−2i2i2i−2i−2i-111-1-2211-1-100000000i−2i−i−i2iiii−i−i−i−iii−333−300−3−3330033−3−30000000000000000i3−i3−i3i30000
χ6144444-24-4-4-2-244444-24-4-4-4-4-24-2-2-2-2-2-24-244-4-42-4-422-4-422200000000-2-2-2-222222200000000000000000000000000000000000000000000000000000000000000
χ6244444-2-244-2-24-244-2-2-24444-2-21-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-200000000111111111144-2-2-2-200000000000000000000000000000000-2-21111000000000000000000
χ6344444-2-244-2-24-244-2-2-24444-2-21-2-211-2-21-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000001111111111-4-422220000000000000000000000000000000022-1-1-1-1000000000000000000
χ6444444-2-2-4-4-2-24-244-2-2-2-4-4-4-4-2-21-2-211-2-21-2-2222222222222000000001111-1-1-1-1-1-100−2i32i3−2i32i30000000000000000000000000000000000i3−i3i3−i3000000000000000000
χ6544444-2-2-4-4-2-24-244-2-2-2-4-4-4-4-2-21-2-211-2-21-2-2222222222222000000001111-1-1-1-1-1-1002i3−2i32i3−2i30000000000000000000000000000000000−i3i3−i3i3000000000000000000
χ664444-24-24444-2-2-2-2-24-2-2-2-2-2-21-2-2-2-2-2-21-211-2-2411-2-2114-2-24444-2-2-2-21111-2-2111100000000-2-2-2-2-2-2111111110000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.