Finite Group Databasebeta

← Group #13155705

Character table — Group #13155705

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order1222333446666666661212121233366666666612121212121212121212121244441212121236661212121212124488121212121212121212121212121212121212242424242424242424242424242424241212121212124444881212121224242424121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111
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
χ91-1-111111-111-1-1-1-1-1-1111-1-1111-1-1-1111-1-1-1-11-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-1i−i1-1ii−i−ii−iii−i−iiiii−i−i−i−i11-1-1111111-1-1-1-1-1-1i−iii−i−ii−i1-1i−i11-1-1ii−i−ii−i1-1
χ101-1-111111-111-1-1-1-1-1-1111-1-1111-1-1-1111-1-1-1-11-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-1i−i-11ii−i−ii−iii−i−iiiii−i−i−i−i-1-111-1-1-1-1-1-1111111i−iii−i−i−ii1-1−ii11-1-1−i−iii−ii-11
χ111-1-111111-111-1-1-1-1-1-1111-1-1111-1-1-1111-1-1-1-11-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-1−ii1-1ii−i−ii−i−i−iiiiiii−i−i−i−i11-1-1111111-1-1-1-1-1-1−ii−i−iii−ii-11i−i-1-111ii−i−i−ii-11
χ121-1-111111-111-1-1-1-1-1-1111-1-1111-1-1-1111-1-1-1-11-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-1−ii-11ii−i−ii−i−i−iiiiiii−i−i−i−i-1-111-1-1-1-1-1-1111111−ii−i−iiii−i-11−ii-1-111−i−iiii−i1-1
χ131-1-111111-111-1-1-1-1-1-1111-1-1111-1-1-1111-1-1-1-11-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-1i−i1-1−i−iii−iiii−i−i−i−i−i−iiiii11-1-1111111-1-1-1-1-1-1i−iii−i−ii−i-11−ii-1-111−i−iiii−i-11
χ141-1-111111-111-1-1-1-1-1-1111-1-1111-1-1-1111-1-1-1-11-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-1i−i-11−i−iii−iiii−i−i−i−i−i−iiiii-1-111-1-1-1-1-1-1111111i−iii−i−i−ii-11i−i-1-111ii−i−i−ii1-1
χ151-1-111111-111-1-1-1-1-1-1111-1-1111-1-1-1111-1-1-1-11-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-1−ii1-1−i−iii−ii−i−iii−i−i−i−iiiii11-1-1111111-1-1-1-1-1-1−ii−i−iii−ii1-1−ii11-1-1−i−iii−ii1-1
χ161-1-111111-111-1-1-1-1-1-1111-1-1111-1-1-1111-1-1-1-11-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-1−ii-11−i−iii−ii−i−iii−i−i−i−iiiii-1-111-1-1-1-1-1-1111111−ii−i−iiii−i1-1i−i11-1-1ii−i−ii−i-11
χ172222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-2-2-200002-22-222000022-2-222-2-20000000000000000000000000000000000000000
χ182222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-20000-22-22-2-20000-2-222-2-2220000000000000000000000000000000000000000
χ19222222-1222222-12-12-122222-1-122-12-1-1-1-1-12-1-1-1-122-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-1002200-1-1-1-100000000
χ20222222-1222222-12-12-122222-1-122-12-1-1-1-1-12-1-1-1-122-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2002222-1-11111-1-1-1-1-1-1-1-10000000000000000-2-2111100-2-200111100000000
χ21222222-1222222-12-12-122222-1-122-12-1-1-1-1-12-1-1-1-122-1-1222-2-2-2-21111-1-1-1-1-1-1-1-1-1-12200-2-2-2-211-1-1-1-111111111000000000000000022-1-1-1-100-2-200111100000000
χ22222222-1222222-12-12-122222-1-122-12-1-1-1-1-12-1-1-1-122-1-1222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2111111111111110000000000000000-2-21111002200-1-1-1-100000000
χ23222222-1-2-22222-12-12-1-2-2-2-22-1-122-12-1-1-1-1-1-21111-2-211-2-2-222-2-21111-1-1-1-111111100002-22-2-1-1−i3i3−i3i3-1-111-1-111000000000000000000−i3i3−i3i3000000−i3i3−i3i300000000
χ24222222-1-2-22222-12-12-1-2-2-2-22-1-122-12-1-1-1-1-1-21111-2-211-2-2-222-2-21111-1-1-1-111111100002-22-2-1-1i3−i3i3−i3-1-111-1-111000000000000000000i3−i3i3−i3000000i3−i3i3−i300000000
χ25222222-1-2-22222-12-12-1-2-2-2-22-1-122-12-1-1-1-1-1-21111-2-211-2-2-2-2-222-1-1-1-1-1-1-1-11111110000-22-2211−i3i3−i3i311-1-111-1-1000000000000000000−i3i3−i3i3000000i3−i3i3−i300000000
χ26222222-1-2-22222-12-12-1-2-2-2-22-1-122-12-1-1-1-1-1-21111-2-211-2-2-2-2-222-1-1-1-1-1-1-1-11111110000-22-2211i3−i3i3−i311-1-111-1-1000000000000000000i3−i3i3−i3000000−i3i3−i3i300000000
χ2722222-12222-1222-12-122222-12-1-1-1-1-12-122-1-12222-1-122-1-1-100000000-1-1-1-1-1-1-1-1-1-122220000002222000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122000000000000-1-100
χ2822222-12222-1222-12-122222-12-1-1-1-1-12-122-1-12222-1-122-1-1-100000000-1-1-1-1-1-1-1-1-1-122-2-2000000222200000000-2-2-2-2111111111111-1-1-1-1-1-1-2-20000000000001100
χ2922222-12222-1222-12-122222-12-1-1-1-1-12-122-1-12222-1-122-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-222000000-2-2-2-2000000002222-1-1-1-1-1-1-1-1-1-1-1-1111111-2-20000000000001100
χ3022222-12222-1222-12-122222-12-1-1-1-1-12-122-1-12222-1-122-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2-2-2000000-2-2-2-200000000-2-2-2-211111111111111111122000000000000-1-100
χ312222-12222-12-1-122222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-122222222-1-1-1-122-1-1-1-10022-1-1-1-1220000-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000000000220000-1-1-1-10000
χ322222-12222-12-1-122222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-122222222-1-1-1-122-1-1-1-100-2-2-1-1-1-1220000-1-1-1-1-1-1-1-11111-2-21111-2-211110000000000-2-2000011110000
χ332222-12222-12-1-122222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-100221111-2-2000011111111-1-1-1-122-1-1-1-122-1-1-1-10000000000-2-2000011110000
χ342222-12222-12-1-122222-1-1-1-1-1-12-1-12-1-12-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-100-2-21111-2-20000111111111111-2-21111-2-211110000000000220000-1-1-1-10000
χ352222-122-2-2-12-1-1222221111-1-12-1-12-1-12-1-12-2-2-2111111-21122-2-2-2-2-2-2-1-1-1-1-2-211110000-11-11220000-1-111-1-1113−33−30033−3−30033−3−300000000000000003−33−30000
χ362222-122-2-2-12-1-1222221111-1-12-1-12-1-12-1-12-2-2-2111111-21122-2-2-2-2-2-2-1-1-1-1-2-211110000-11-11220000-1-111-1-111−33−3300−3−33300−3−3330000000000000000−33−330000
χ372222-122-2-2-12-1-1222221111-1-12-1-12-1-12-1-12-2-2-2111111-211-2-2222222-1-1-1-1-2-2111100001-11-1-2-2000011-1-111-1-13−33−30033−3−30033−3−30000000000000000−33−330000
χ382222-122-2-2-12-1-1222221111-1-12-1-12-1-12-1-12-2-2-2111111-211-2-2222222-1-1-1-1-2-2111100001-11-1-2-2000011-1-111-1-1−33−3300−3−33300−3−33300000000000000003−33−30000
χ392-2-22222-2222-2-2-2-2-2-22-2-222222-2-2-2222-2-2-22-22-2-22222-2-2-22i−2i−2i2i−2i−2i2i2i2-2-22-22-2-22200002i−2i−2i2i2i−2i00002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ402-2-22222-2222-2-2-2-2-2-22-2-222222-2-2-2222-2-2-22-22-2-22222-2-2-2−2i2i2i−2i2i2i−2i−2i2-2-22-22-2-2220000−2i2i2i−2i−2i2i0000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ412-2-2222-12-222-2-21-21-2-122-2-22-1-1-2-212-1-1111-2-11-1-1-2-2112222i−2i2i−2i−i−iii-111-1-11-1-1112i−2i002i2i−2i−2i−ii−i−iii−i−i−i−iiiii00000000000000002i−2i−i−iii002-200-1-11100000000
χ422-2-2222-12-222-2-21-21-2-122-2-22-1-1-2-212-1-1111-2-11-1-1-2-2112222i−2i2i−2i−i−iii-111-1-11-1-111−2i2i002i2i−2i−2i−iiii−i−i−i−i−i−iiiii0000000000000000−2i2iii−i−i00-220011-1-100000000
χ432-2-2222-12-222-2-21-21-2-122-2-22-1-1-2-212-1-1111-2-11-1-1-2-211222−2i2i−2i2iii−i−i-111-1-11-1-1112i−2i00−2i−2i2i2ii−i−i−iiiiiii−i−i−i−i00000000000000002i−2i−i−iii00-220011-1-100000000
χ442-2-2222-12-222-2-21-21-2-122-2-22-1-1-2-212-1-1111-2-11-1-1-2-211222−2i2i−2i2iii−i−i-111-1-11-1-111−2i2i00−2i−2i2i2ii−iii−i−iiiii−i−i−i−i0000000000000000−2i2iii−i−i002-200-1-11100000000
χ452-2-2222-1-2222-2-21-21-2-1-2-2222-1-1-2-212-1-111121-11122-1-1-2-2-22i−2i−2i2iii−i−i-111-11-111-1-100002i−2i−2i2i−ii3−3−33−i−iiiii−i−i0000000000000000003−3−33000000−i3i3i3−i300000000
χ462-2-2222-1-2222-2-21-21-2-1-2-2222-1-1-2-212-1-111121-11122-1-1-2-2-22i−2i−2i2iii−i−i-111-11-111-1-100002i−2i−2i2i−ii−333−3−i−iiiii−i−i000000000000000000−333−3000000i3−i3−i3i300000000
χ472-2-2222-1-2222-2-21-21-2-1-2-2222-1-1-2-212-1-111121-11122-1-1-2-2-2−2i2i2i−2i−i−iii-111-11-111-1-10000−2i2i2i−2ii−i3−3−33ii−i−i−i−iii0000000000000000003−3−33000000i3−i3−i3i300000000
χ482-2-2222-1-2222-2-21-21-2-1-2-2222-1-1-2-212-1-111121-11122-1-1-2-2-2−2i2i2i−2i−i−iii-111-11-111-1-10000−2i2i2i−2ii−i−333−3ii−i−i−i−iii000000000000000000−333−3000000−i3i3i3−i300000000
χ492-2-222-122-22-1-2-2-21-21222-2-2-12-1111-12-1-2-2112-22211-2-2-1-1-100000000-111-1-11-1-1112i−2i2-20000002i2i−2i−2i0000000022-2-2-1-1-1-1-1-1111111−ii−i−iii2i−2i000000000000−ii00
χ502-2-222-122-22-1-2-2-21-21222-2-2-12-1111-12-1-2-2112-22211-2-2-1-1-100000000-111-1-11-1-1112i−2i-220000002i2i−2i−2i00000000-2-222111111-1-1-1-1-1-1−ii−i−iii−2i2i000000000000i−i00
χ512-2-222-122-22-1-2-2-21-21222-2-2-12-1111-12-1-2-2112-22211-2-2-1-1-100000000-111-1-11-1-111−2i2i2-2000000−2i−2i2i2i0000000022-2-2-1-1-1-1-1-1111111i−iii−i−i−2i2i000000000000i−i00
χ522-2-222-122-22-1-2-2-21-21222-2-2-12-1111-12-1-2-2112-22211-2-2-1-1-100000000-111-1-11-1-111−2i2i-22000000−2i−2i2i2i00000000-2-222111111-1-1-1-1-1-1i−iii−i−i2i−2i000000000000−ii00
χ532-2-22-1222-2-1211-2-2-2-22-1-111-1-1211-2-1-1211-2-22-2-1-111112-1-12i−2i2i−2i2i2i−2i−2i-111-12-2-1-111002-2−i−iii2i−2i0000−i−i−i−iiiii-1-11122-1-1-1-1-2-2111100000000002i−2i0000−i−iii0000
χ542-2-22-1222-2-1211-2-2-2-22-1-111-1-1211-2-1-1211-2-22-2-1-111112-1-12i−2i2i−2i2i2i−2i−2i-111-12-2-1-11100-22−i−iii2i−2i0000−i−i−i−iiiii11-1-1-2-2111122-1-1-1-10000000000−2i2i0000ii−i−i0000
χ552-2-22-1222-2-1211-2-2-2-22-1-111-1-1211-2-1-1211-2-22-2-1-111112-1-1−2i2i−2i2i−2i−2i2i2i-111-12-2-1-111002-2ii−i−i−2i2i0000iiii−i−i−i−i-1-11122-1-1-1-1-2-211110000000000−2i2i0000ii−i−i0000
χ562-2-22-1222-2-1211-2-2-2-22-1-111-1-1211-2-1-1211-2-22-2-1-111112-1-1−2i2i−2i2i−2i−2i2i2i-111-12-2-1-11100-22ii−i−i−2i2i0000iiii−i−i−i−i11-1-1-2-2111122-1-1-1-100000000002i−2i0000−i−iii0000
χ572-2-22-122-22-1211-2-2-2-2211-1-1-1-1211-2-1-1211-22-2211-1-1-1-1-2112i−2i−2i2i−2i−2i2i2i-111-1-2211-1-10000−iii−i2i−2i0000−i−iiiii−i−i3−3−330033−3−300−3−3330000000000000000i3−i3−i3i30000
χ582-2-22-122-22-1211-2-2-2-2211-1-1-1-1211-2-1-1211-22-2211-1-1-1-1-2112i−2i−2i2i−2i−2i2i2i-111-1-2211-1-10000−iii−i2i−2i0000−i−iiiii−i−i−333−300−3−3330033−3−30000000000000000−i3i3i3−i30000
χ592-2-22-122-22-1211-2-2-2-2211-1-1-1-1211-2-1-1211-22-2211-1-1-1-1-211−2i2i2i−2i2i2i−2i−2i-111-1-2211-1-10000i−i−ii−2i2i0000ii−i−i−i−iii3−3−330033−3−300−3−3330000000000000000−i3i3i3−i30000
χ602-2-22-122-22-1211-2-2-2-2211-1-1-1-1211-2-1-1211-22-2211-1-1-1-1-211−2i2i2i−2i2i2i−2i−2i-111-1-2211-1-10000i−i−ii−2i2i0000ii−i−i−i−iii−333−300−3−3330033−3−30000000000000000i3−i3−i3i30000
χ6144444-24-4-44-2444-24-24-4-4-4-4-24-2-2-2-2-24-244-22-4-4-4-422-4-422200000000-2-2-2-222222200000000000000000000000000000000000000000000000000000000000000
χ6244444-2-2444-244-2-2-2-2-24444-2-21-2-21-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-20000000011111111114400000000-2-2-2-2000000000000000000000000-2-21111000000000000000000
χ6344444-2-2444-244-2-2-2-2-24444-2-21-2-21-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-2000000001111111111-4-400000000222200000000000000000000000022-1-1-1-1000000000000000000
χ6444444-2-2-4-44-244-2-2-2-2-2-4-4-4-4-2-21-2-21-2-21-2-21222222222222000000001111-1-1-1-1-1-10000000000−2i32i3−2i32i300000000000000000000000000i3−i3i3−i3000000000000000000
χ6544444-2-2-4-44-244-2-2-2-2-2-4-4-4-4-2-21-2-21-2-21-2-21222222222222000000001111-1-1-1-1-1-100000000002i3−2i32i3−2i300000000000000000000000000−i3i3−i3i3000000000000000000
χ664444-24-244-24-2-2-24-24-2-2-2-2-2-21-2-2-2-2-21-211-24-2-211-2-2114-2-24444-2-2-2-21111-2-211110000-2-2-2-2-2-20000111111110000000000000000000000000000000000000000
χ674444-24-244-24-2-2-24-24-2-2-2-2-2-21-2-2-2-2-21-211-24-2-211-2-2114-2-2-4-4-4-422221111-2-2111100002222220000-1-1-1-1-1-1-1-10000000000000000000000000000000000000000
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χ1258-8-88-4-4-48-8-4-4444444-4-4-444222-2-2-2222-2-2-24-4422-2-2-2-2-42200000000-111-12-2-1-11100000000000000000000000000000000000000000000000000000000000000
χ1268-8-88-4-4-4-88-4-4444444-444-4-4222-2-2-2222-2-2-2-44-4-2-222224-2-200000000-111-1-2211-1-100000000000000000000000000000000000000000000000000000000000000

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