Finite Group Databasebeta

← Group #13155704

Character table — Group #13155704

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order1222333446666666661212121233366666666612121212121212121212121244441212121236661212121212124488121212121212121212121212121212121212242424242424242424242424242424241212121212124444881212121224242424121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-111
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
χ91-1-11111-11-11-1-1-111-1-1-1-111111-1-1-1-111-1-1111-11111-1-1-1-1-1ii−i−iii−i−i1-1-111-111-1-11-1i−iii−i−i11-1-1i−iiiii−i−i−i−iii−i−iiiiiii−i−i−i−i−i−i1-111-1-1i−ii−i1-1ii−i−i11-1-1i−i1-1
χ101-1-11111-11-11-1-1-111-1-1-1-111111-1-1-1-111-1-1111-11111-1-1-1-1-1ii−i−iii−i−i1-1-111-111-1-11-1−iiii−i−i11-1-1i−iiiii−i−i−i−i−i−iii−i−i−i−i−i−iiiiiii1-111-1-1i−i−ii-11ii−i−i-1-111−ii-11
χ111-1-11111-11-11-1-1-111-1-1-1-111111-1-1-1-111-1-1111-11111-1-1-1-1-1ii−i−iii−i−i1-1-111-111-1-1-11i−iii−i−i-1-111i−iiiii−i−i−i−iii−i−iiiiiii−i−i−i−i−i−i-11-1-111−ii−ii1-1−i−iii11-1-1−ii-11
χ121-1-11111-11-11-1-1-111-1-1-1-111111-1-1-1-111-1-1111-11111-1-1-1-1-1ii−i−iii−i−i1-1-111-111-1-1-11−iiii−i−i-1-111i−iiiii−i−i−i−i−i−iii−i−i−i−i−i−iiiiiii-11-1-111−iii−i-11−i−iii-1-111i−i1-1
χ131-1-11111-11-11-1-1-111-1-1-1-111111-1-1-1-111-1-1111-11111-1-1-1-1-1−i−iii−i−iii1-1-111-111-1-11-1i−i−i−iii11-1-1−ii−i−i−i−iiiiiii−i−iiiiiii−i−i−i−i−i−i1-111-1-1−iii−i-11−i−iii-1-111i−i-11
χ141-1-11111-11-11-1-1-111-1-1-1-111111-1-1-1-111-1-1111-11111-1-1-1-1-1−i−iii−i−iii1-1-111-111-1-11-1−ii−i−iii11-1-1−ii−i−i−i−iiiii−i−iii−i−i−i−i−i−iiiiiii1-111-1-1−ii−ii1-1−i−iii11-1-1−ii1-1
χ151-1-11111-11-11-1-1-111-1-1-1-111111-1-1-1-111-1-1111-11111-1-1-1-1-1−i−iii−i−iii1-1-111-111-1-1-11i−i−i−iii-1-111−ii−i−i−i−iiiiiii−i−iiiiiii−i−i−i−i−i−i-11-1-111i−i−ii-11ii−i−i-1-111−ii1-1
χ161-1-11111-11-11-1-1-111-1-1-1-111111-1-1-1-111-1-1111-11111-1-1-1-1-1−i−iii−i−iii1-1-111-111-1-1-11−ii−i−iii-1-111−ii−i−i−i−iiiii−i−iii−i−i−i−i−i−iiiiiii-11-1-111i−ii−i1-1ii−i−i11-1-1i−i-11
χ172222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22-22-222222222-2-2-2-2-2-200002-22-20000-2-222-2-222-2-20000000000000000000000000000000000000000
χ182222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-22-22-2-2-2-22222-2-2-2-2-2-20000-22-22000022-2-222-2-2220000000000000000000000000000000000000000
χ19222222-1222222-12-12-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-1220000-1-1-1-100000000
χ20222222-1222222-12-12-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20022221111-1-1-1-1-1-1-1-1-1-10000000000000000-2-21111-2-20000111100000000
χ21222222-1222222-12-12-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-1222-2-2-2-21111-1-1-1-1-1-1-1-1-1-12200-2-2-2-2-1-1-1-11111111111000000000000000022-1-1-1-1-2-20000111100000000
χ22222222-1222222-12-12-122222-1-122-1-12-1-1-1-12-1-122-1-1-1-1222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2111111111111110000000000000000-2-21111220000-1-1-1-100000000
χ23222222-1-2-22222-12-12-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-22-22-2-1-1-1-1-1-1-1-111111100002-22-2−i3i3−i3i311-1-111-1-111000000000000000000−i3i3−i3i3000000−i3i3−i3i300000000
χ24222222-1-2-22222-12-12-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-22-22-2-1-1-1-1-1-1-1-111111100002-22-2i3−i3i3−i311-1-111-1-111000000000000000000i3−i3i3−i3000000i3−i3i3−i300000000
χ25222222-1-2-22222-12-12-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-2-22-221111-1-1-1-11111110000-22-22−i3i3−i3i3-1-111-1-111-1-1000000000000000000−i3i3−i3i3000000i3−i3i3−i300000000
χ26222222-1-2-22222-12-12-1-2-2-2-22-1-122-1-12-1-1-1-1-211-2-21111-2-2-2-22-221111-1-1-1-11111110000-22-22i3−i3i3−i3-1-111-1-111-1-1000000000000000000i3−i3i3−i3000000−i3i3−i3i300000000
χ2722222-12222-1-1-122222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-122222222-1-1-1-122-1-1-1-10022-1-1-1-1000022-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000000000220000-1-1-1-10000
χ2822222-12222-1-1-122222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-122222222-1-1-1-122-1-1-1-100-2-2-1-1-1-1000022-1-1-1-1-1-1-1-11111-2-21111-2-211110000000000-2-2000011110000
χ2922222-12222-1-1-122222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-1002211110000-2-211111111-1-1-1-122-1-1-1-122-1-1-1-10000000000-2-2000011110000
χ3022222-12222-1-1-122222-1-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-100-2-211110000-2-2111111111111-2-21111-2-211110000000000220000-1-1-1-10000
χ3122222-12-2-22-1-1-1222221111-12-1-1-122-1-1-1-12-2-2-2111111-2112-22-22222-1-1-1-1-2-211110000-11-110000-2-2-1-111-1-1113−33−30033−3−30033−3−300000000000000003−33−30000
χ3222222-12-2-22-1-1-1222221111-12-1-1-122-1-1-1-12-2-2-2111111-2112-22-22222-1-1-1-1-2-211110000-11-110000-2-2-1-111-1-111−33−3300−3−33300−3−3330000000000000000−33−330000
χ3322222-12-2-22-1-1-1222221111-12-1-1-122-1-1-1-12-2-2-2111111-211-22-22-2-2-2-2-1-1-1-1-2-2111100001-11-100002211-1-111-1-13−33−30033−3−30033−3−30000000000000000−33−330000
χ3422222-12-2-22-1-1-1222221111-12-1-1-122-1-1-1-12-2-2-2111111-211-22-22-2-2-2-2-1-1-1-1-2-2111100001-11-100002211-1-111-1-1−33−3300−3−33300−3−33300000000000000003−33−30000
χ352222-12222-12222-12-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-100000000-1-1-1-1-1-1-1-1-1-122220000222200000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100220000000000-1-100
χ362222-12222-12222-12-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-100000000-1-1-1-1-1-1-1-1-1-122-2-2000022220000000000-2-2-2-2111111111111-1-1-1-1-1-100-2-200000000001100
χ372222-12222-12222-12-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2220000-2-2-2-200000000002222-1-1-1-1-1-1-1-1-1-1-1-111111100-2-200000000001100
χ382222-12222-12222-12-122222-1-12-1-1-1-1-1222-1-122-1-12222-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-20000000000-2-2-2-211111111111111111100220000000000-1-100
χ392-2-222222-2-22-2-2-222-2-222-2-2222-2-2-2-222-2-22-2-22-2-2-2-2222222i−2i−2i2i2i2i−2i−2i2-2-22-22-2-22200002i−2i−2i2i0000−2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ402-2-222222-2-22-2-2-222-2-222-2-2222-2-2-2-222-2-22-2-22-2-2-2-222222−2i2i2i−2i−2i−2i2i2i2-2-22-22-2-2220000−2i2i2i−2i00002i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ412-2-2222-12-2-22-2-212-1-2122-2-22-1-1-2-2112-111-1-21-1-2-211-1-12222i−2i−2i2i−i−iii-111-11-111-1-100002i−2i−2i2i−i3i3i3−i3i−i−i−iiiii−i−i000000000000000000−i3i3i3−i30000003−3−3300000000
χ422-2-2222-12-2-22-2-212-1-2122-2-22-1-1-2-2112-111-1-21-1-2-211-1-12222i−2i−2i2i−i−iii-111-11-111-1-100002i−2i−2i2ii3−i3−i3i3i−i−i−iiiii−i−i000000000000000000i3−i3−i3i3000000−333−300000000
χ432-2-2222-12-2-22-2-212-1-2122-2-22-1-1-2-2112-111-1-21-1-2-211-1-1222−2i2i2i−2iii−i−i-111-11-111-1-10000−2i2i2i−2i−i3i3i3−i3−iiii−i−i−i−iii000000000000000000−i3i3i3−i3000000−333−300000000
χ442-2-2222-12-2-22-2-212-1-2122-2-22-1-1-2-2112-111-1-21-1-2-211-1-1222−2i2i2i−2iii−i−i-111-11-111-1-10000−2i2i2i−2ii3−i3−i3i3−iiii−i−i−i−iii000000000000000000i3−i3−i3i30000003−3−3300000000
χ452-2-2222-1-22-22-2-212-1-21-2-2222-1-1-2-2112-111-12-1122-1-111-2-2-22i2i−2i−2i−i−iii-111-1-11-1-1112-2002i2i−2i−2i-1-111−ii−i−i−i−iiiii00000000000000002-2-1-1112i−2i0000−i−iii00000000
χ462-2-2222-1-22-22-2-212-1-21-2-2222-1-1-2-2112-111-12-1122-1-111-2-2-22i2i−2i−2i−i−iii-111-1-11-1-111-22002i2i−2i−2i11-1-1−ii−i−i−i−iiiii0000000000000000-2211-1-1−2i2i0000ii−i−i00000000
χ472-2-2222-1-22-22-2-212-1-21-2-2222-1-1-2-2112-111-12-1122-1-111-2-2-2−2i−2i2i2iii−i−i-111-1-11-1-1112-200−2i−2i2i2i-1-111i−iiiii−i−i−i−i00000000000000002-2-1-111−2i2i0000ii−i−i00000000
χ482-2-2222-1-22-22-2-212-1-21-2-2222-1-1-2-2112-111-12-1122-1-111-2-2-2−2i−2i2i2iii−i−i-111-1-11-1-111-2200−2i−2i2i2i11-1-1i−iiiii−i−i−i−i0000000000000000-2211-1-12i−2i0000−i−iii00000000
χ492-2-222-122-2-2-111-222-2-2-1-111-12-111-2-2-1-1112-2-221111-1-12-1-12i−2i−2i2i2i2i−2i−2i-111-1-2211-1-10000−iii−i0000−2i2i−i−iiiii−i−i−i3i3i3−i300−i3−i3i3i300i3i3−i3−i30000000000000000−333−30000
χ502-2-222-122-2-2-111-222-2-2-1-111-12-111-2-2-1-1112-2-221111-1-12-1-12i−2i−2i2i2i2i−2i−2i-111-1-2211-1-10000−iii−i0000−2i2i−i−iiiii−i−ii3−i3−i3i300i3i3−i3−i300−i3−i3i3i300000000000000003−3−330000
χ512-2-222-122-2-2-111-222-2-2-1-111-12-111-2-2-1-1112-2-221111-1-12-1-1−2i2i2i−2i−2i−2i2i2i-111-1-2211-1-10000i−i−ii00002i−2iii−i−i−i−iii−i3i3i3−i300−i3−i3i3i300i3i3−i3−i300000000000000003−3−330000
χ522-2-222-122-2-2-111-222-2-2-1-111-12-111-2-2-1-1112-2-221111-1-12-1-1−2i2i2i−2i−2i−2i2i2i-111-1-2211-1-10000i−i−ii00002i−2iii−i−i−i−iiii3−i3−i3i300i3i3−i3−i300−i3−i3i3i30000000000000000−333−30000
χ532-2-222-12-22-2-111-222-2-211-1-1-12-111-2-2-1-111222-2-1-1-1-111-2112i2i−2i−2i2i2i−2i−2i-111-12-2-1-111002i−2i−i−iii00002i−2i−i−i−i−iiiii−i−iii2i2i−i−i−i−i−2i−2iiiii00000000002-20000-1-1110000
χ542-2-222-12-22-2-111-222-2-211-1-1-12-111-2-2-1-111222-2-1-1-1-111-2112i2i−2i−2i2i2i−2i−2i-111-12-2-1-11100−2i2i−i−iii00002i−2i−i−i−i−iiiiiii−i−i−2i−2iiiii2i2i−i−i−i−i0000000000-22000011-1-10000
χ552-2-222-12-22-2-111-222-2-211-1-1-12-111-2-2-1-111222-2-1-1-1-111-211−2i−2i2i2i−2i−2i2i2i-111-12-2-1-111002i−2iii−i−i0000−2i2iiiii−i−i−i−i−i−iii2i2i−i−i−i−i−2i−2iiiii0000000000-22000011-1-10000
χ562-2-222-12-22-2-111-222-2-211-1-1-12-111-2-2-1-111222-2-1-1-1-111-211−2i−2i2i2i−2i−2i2i2i-111-12-2-1-11100−2i2iii−i−i0000−2i2iiiii−i−i−i−iii−i−i−2i−2iiiii2i2i−i−i−i−i00000000002-20000-1-1110000
χ572-2-22-122-2212-2-2-2-121-2-2-222-1-121111-12-2-2-1-12-2-1-122-2-211100000000-111-1-11-1-1112-22i−2i000022-2-200000000002i2i−2i−2i−i−i−i−i−i−iiiiiii-11-1-111002i−2i0000000000−ii00
χ582-2-22-122-2212-2-2-2-121-2-2-222-1-121111-12-2-2-1-12-2-1-122-2-211100000000-111-1-11-1-1112-2−2i2i000022-2-20000000000−2i−2i2i2iiiiiii−i−i−i−i−i−i-11-1-11100−2i2i0000000000i−i00
χ592-2-22-122-2212-2-2-2-121-2-2-222-1-121111-12-2-2-1-12-2-1-122-2-211100000000-111-1-11-1-111-222i−2i0000-2-22200000000002i2i−2i−2i−i−i−i−i−i−iiiiiii1-111-1-100−2i2i0000000000i−i00
χ602-2-22-122-2212-2-2-2-121-2-2-222-1-121111-12-2-2-1-12-2-1-122-2-211100000000-111-1-11-1-111-22−2i2i0000-2-2220000000000−2i−2i2i2iiiiiii−i−i−i−i−i−i1-111-1-1002i−2i0000000000−ii00
χ6144444-2-2444-2-2-2-24-24-2-2-2-2-2-2-21-2-2-2-2-2111-24-2-2-2-211114-2-24444-2-2-2-21111-2-211110000-2-2-2-20000-2-2111111110000000000000000000000000000000000000000
χ6244444-2-2444-2-2-2-24-24-2-2-2-2-2-2-21-2-2-2-2-2111-24-2-2-2-211114-2-2-4-4-4-422221111-2-2111100002222000022-1-1-1-1-1-1-1-10000000000000000000000000000000000000000
χ6344444-2-2-4-44-2-2-2-24-24-22222-2-21-2-2-2-2-2111-2-42222-1-1-1-1-4224-44-4-2-2-2-2111122-1-1-1-10000-22-2200002211-1-111-1-10000000000000000000000000000000000000000
χ6444444-2-2-4-44-2-2-2-24-24-22222-2-21-2-2-2-2-2111-2-42222-1-1-1-1-422-44-442222111122-1-1-1-100002-22-20000-2-2-1-111-1-1110000000000000000000000000000000000000000
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χ1268-8-88-4-4-4-884-4444-4-44444-4-4222-2-2-2-222-2-22-4-442222-2-24-2-200000000-111-12-2-1-11100000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.