Finite Group Databasebeta

← Group #13155672

Character table — Group #13155672

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size1111222222222222222222444444444444444444444444666666668888888888121212121212121212121212121212121212121212121212121212121212121212121212121224242424242436363636363636363636363636367272108108
order12223334466666666612121212333666666666121212121212121212121212444412121212366612121212121244881212121212121212121212121212121212122424242424242424242424242424242412121212121222448812121212242424246644
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
χ31111111111111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111
χ71111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111
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
χ91-11-11111-1-1-11-1-1-111-111-1-1111-1-1-1-111-1-111-1-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-11-11-1ii−i−i11-1-1i−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
χ101-11-11111-1-1-11-1-1-111-111-1-1111-1-1-1-111-1-111-1-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-11-1-11ii−i−i11-1-1i−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
χ111-11-11111-1-1-11-1-1-111-111-1-1111-1-1-1-111-1-111-1-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-1-111-1ii−i−i-1-111i−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
χ121-11-11111-1-1-11-1-1-111-111-1-1111-1-1-1-111-1-111-1-111-1-1-1-1111i−ii−iii−i−i1-1-111-111-1-1-11-11ii−i−i-1-111i−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
χ131-11-11111-1-1-11-1-1-111-111-1-1111-1-1-1-111-1-111-1-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-11-11-1−i−iii11-1-1−ii−i−i−i−iiiii11-1-1111111-1-1-1-1-1-11-111-1-11-1−ii−ii−i−iii−i−iii1-1−ii
χ141-11-11111-1-1-11-1-1-111-111-1-1111-1-1-1-111-1-111-1-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-11-1-11−i−iii11-1-1−ii−i−i−i−iiiii-1-111-1-1-1-1-1-11111111-111-1-1-11−iii−i−i−iiiii−i−i-11i−i
χ151-11-11111-1-1-11-1-1-111-111-1-1111-1-1-1-111-1-111-1-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-1-111-1−i−iii-1-111−ii−i−i−i−iiiii11-1-1111111-1-1-1-1-1-1-11-1-111-11i−i−iiii−i−i−i−iii-11i−i
χ161-11-11111-1-1-11-1-1-111-111-1-1111-1-1-1-111-1-111-1-111-1-1-1-1111−ii−ii−i−iii1-1-111-111-1-1-11-11−i−iii-1-111−ii−i−i−i−iiiii-1-111-1-1-1-1-1-1111111-11-1-1111-1i−ii−iii−i−iii−i−i1-1−ii
χ172222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-222222222-2-2-2-2-2-200002-22-20000-2-222-2-222-2-20000000000000000000000000000000000000000
χ182222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-22222-2-2-2-2-2-20000-22-22000022-2-222-2-2220000000000000000000000000000000000000000
χ19222222-122-1-122222-1222222-1-1-1-1-1-12-122-122-12222-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-122220000222200000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122000000000000-1-100
χ20222222-122-1-122222-1222222-1-1-1-1-1-12-122-122-12222-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-122-2-2000022220000000000-2-2-2-2111111111111-1-1-1-1-1-1-2-20000000000001100
χ21222222-122-1-122222-1222222-1-1-1-1-1-12-122-122-12222-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2220000-2-2-2-200000000002222-1-1-1-1-1-1-1-1-1-1-1-1111111-2-20000000000001100
χ22222222-122-1-122222-1222222-1-1-1-1-1-12-122-122-12222-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-2-2-2-20000000000-2-2-2-211111111111111111122000000000000-1-100
χ2322222-122222222-1-12-12222-12-122-1-1-12-1-1-1-1-12-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-122002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000022-1-1-1-1002200-1-1-1-100000000
χ2422222-122222222-1-12-12222-12-122-1-1-12-1-1-1-1-12-1-1-1-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20022221111-1-1-1-1-1-1-1-1-1-10000000000000000-2-2111100-2-200111100000000
χ2522222-122222222-1-12-12222-12-122-1-1-12-1-1-1-1-12-1-1-1-122222-2-2-2-21111-1-1-1-1-1-1-1-1-1-12200-2-2-2-2-1-1-1-11111111111000000000000000022-1-1-1-100-2-200111100000000
χ2622222-122222222-1-12-12222-12-122-1-1-12-1-1-1-1-12-1-1-1-122222-2-2-2-21111-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-2111111111111110000000000000000-2-21111002200-1-1-1-100000000
χ2722222-12-2-222222-1-12-1-2-2-2-2-12-122-1-1-12-1-1-111-21111-2-2-2-2-222-2-2-1-1-1-1-1-1-1-111111100002-22-2−i3i3−i3i311-1-111-1-111000000000000000000−i3i3−i3i3000000−i3i3−i3i300000000
χ2822222-12-2-222222-1-12-1-2-2-2-2-12-122-1-1-12-1-1-111-21111-2-2-2-2-222-2-2-1-1-1-1-1-1-1-111111100002-22-2i3−i3i3−i311-1-111-1-111000000000000000000i3−i3i3−i3000000i3−i3i3−i300000000
χ2922222-12-2-222222-1-12-1-2-2-2-2-12-122-1-1-12-1-1-111-21111-2-2-2-2-2-2-2221111-1-1-1-11111110000-22-22−i3i3−i3i3-1-111-1-111-1-1000000000000000000−i3i3−i3i3000000i3−i3i3−i300000000
χ3022222-12-2-222222-1-12-1-2-2-2-2-12-122-1-1-12-1-1-111-21111-2-2-2-2-2-2-2221111-1-1-1-11111110000-22-22i3−i3i3−i3-1-111-1-111-1-1000000000000000000i3−i3i3−i3000000−i3i3−i3i300000000
χ312222-1222222-1-1-12222-1-1-1-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-12-1-122222222-1-1-1-122-1-1-1-10022-1-1-1-1000022-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-10000000000220000-1-1-1-10000
χ322222-1222222-1-1-12222-1-1-1-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-12-1-122222222-1-1-1-122-1-1-1-100-2-2-1-1-1-1000022-1-1-1-1-1-1-1-11111-2-21111-2-211110000000000-2-2000011110000
χ332222-1222222-1-1-12222-1-1-1-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-1002211110000-2-211111111-1-1-1-122-1-1-1-122-1-1-1-10000000000-2-2000011110000
χ342222-1222222-1-1-12222-1-1-1-1-1-12-1-122-1-1-1-12222-1-1-1-1-1-12-1-1-2-2-2-2-2-2-2-2-1-1-1-122-1-1-1-100-2-211110000-2-2111111111111-2-21111-2-211110000000000220000-1-1-1-10000
χ352222-122-2-222-1-1-122221111-1-12-1-122-1-1-1-12-2-2-2111111-21122-2-22222-1-1-1-1-2-211110000-11-110000-2-2-1-111-1-1113−33−30033−3−30033−3−300000000000000003−33−30000
χ362222-122-2-222-1-1-122221111-1-12-1-122-1-1-1-12-2-2-2111111-21122-2-22222-1-1-1-1-2-211110000-11-110000-2-2-1-111-1-111−33−3300−3−33300−3−3330000000000000000−33−330000
χ372222-122-2-222-1-1-122221111-1-12-1-122-1-1-1-12-2-2-2111111-211-2-222-2-2-2-2-1-1-1-1-2-2111100001-11-100002211-1-111-1-13−33−30033−3−30033−3−30000000000000000−33−330000
χ382222-122-2-222-1-1-122221111-1-12-1-122-1-1-1-12-2-2-2111111-211-2-222-2-2-2-2-1-1-1-1-2-2111100001-11-100002211-1-111-1-1−33−3300−3−33300−3−33300000000000000003−33−30000
χ392-22-2222-22-2-22-2-2-222-2-2-222222-2-2-2-222-2-22-222-2-22222-2-2-22i−2i−2i2i2i2i−2i−2i2-2-22-22-2-22200002i−2i−2i2i0000−2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ402-22-2222-22-2-22-2-2-222-2-2-222222-2-2-2-222-2-22-222-2-22222-2-2-2−2i2i2i−2i−2i−2i2i2i2-2-22-22-2-2220000−2i2i2i−2i00002i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ412-22-222-12-2112-2-2-22-1-222-2-22-1-111112-1-2-2-12-2122-2-211-1-1-100000000-111-1-11-1-1112-22-2000022-2-2000000000022-2-2-1-1-1-1-1-1111111-11-1-1112-2000000000000-1100
χ422-22-222-12-2112-2-2-22-1-222-2-22-1-111112-1-2-2-12-2122-2-211-1-1-100000000-111-1-11-1-1112-2-22000022-2-20000000000-2-222111111-1-1-1-1-1-1-11-1-111-220000000000001-100
χ432-22-222-12-2112-2-2-22-1-222-2-22-1-111112-1-2-2-12-2122-2-211-1-1-100000000-111-1-11-1-111-222-20000-2-222000000000022-2-2-1-1-1-1-1-11111111-111-1-1-220000000000001-100
χ442-22-222-12-2112-2-2-22-1-222-2-22-1-111112-1-2-2-12-2122-2-211-1-1-100000000-111-1-11-1-111-22-220000-2-2220000000000-2-222111111-1-1-1-1-1-11-111-1-12-2000000000000-1100
χ452-22-22-122-2-2-22-2-21-12122-2-2-12-1-2-211-1211-1-11-2-1-111-2-22222i−2i2i−2i−i−iii-111-1-11-1-1112-2002i2i−2i−2i-1-111−ii−i−i−i−iiiii00000000000000002-2-1-111002i−2i00−i−iii00000000
χ462-22-22-122-2-2-22-2-21-12122-2-2-12-1-2-211-1211-1-11-2-1-111-2-22222i−2i2i−2i−i−iii-111-1-11-1-111-22002i2i−2i−2i11-1-1−ii−i−i−i−iiiii0000000000000000-2211-1-100−2i2i00ii−i−i00000000
χ472-22-22-122-2-2-22-2-21-12122-2-2-12-1-2-211-1211-1-11-2-1-111-2-2222−2i2i−2i2iii−i−i-111-1-11-1-1112-200−2i−2i2i2i-1-111i−iiiii−i−i−i−i00000000000000002-2-1-11100−2i2i00ii−i−i00000000
χ482-22-22-122-2-2-22-2-21-12122-2-2-12-1-2-211-1211-1-11-2-1-111-2-2222−2i2i−2i2iii−i−i-111-1-11-1-111-2200−2i−2i2i2i11-1-1i−iiiii−i−i−i−i0000000000000000-2211-1-1002i−2i00−i−iii00000000
χ492-22-22-12-22-2-22-2-21-121-2-222-12-1-2-211-1211-11-1211-1-122-2-2-22i−2i−2i2i−i−iii-111-11-111-1-100002i−2i−2i2i−i3i3i3−i3i−i−i−iiiii−i−i000000000000000000−i3i3i3−i30000003−3−3300000000
χ502-22-22-12-22-2-22-2-21-121-2-222-12-1-2-211-1211-11-1211-1-122-2-2-22i−2i−2i2i−i−iii-111-11-111-1-100002i−2i−2i2ii3−i3−i3i3i−i−i−iiiii−i−i000000000000000000i3−i3−i3i3000000−333−300000000
χ512-22-22-12-22-2-22-2-21-121-2-222-12-1-2-211-1211-11-1211-1-122-2-2-2−2i2i2i−2iii−i−i-111-11-111-1-10000−2i2i2i−2i−i3i3i3−i3−iiii−i−i−i−iii000000000000000000−i3i3i3−i3000000−333−300000000
χ522-22-22-12-22-2-22-2-21-121-2-222-12-1-2-211-1211-11-1211-1-122-2-2-2−2i2i2i−2iii−i−i-111-11-111-1-10000−2i2i2i−2ii3−i3−i3i3−iiii−i−i−i−iii000000000000000000i3−i3−i3i30000003−3−3300000000
χ532-22-2-1222-2-2-2-111-222-2-1-111-1-1211-2-2-1-11122-2-2-1-111112-1-12i−2i2i−2i2i2i−2i−2i-111-12-2-1-111002-2−i−iii00002i−2i−i−i−i−iiiii-1-11122-1-1-1-1-2-2111100000000002i−2i0000−i−iii0000
χ542-22-2-1222-2-2-2-111-222-2-1-111-1-1211-2-2-1-11122-2-2-1-111112-1-12i−2i2i−2i2i2i−2i−2i-111-12-2-1-11100-22−i−iii00002i−2i−i−i−i−iiiii11-1-1-2-2111122-1-1-1-10000000000−2i2i0000ii−i−i0000
χ552-22-2-1222-2-2-2-111-222-2-1-111-1-1211-2-2-1-11122-2-2-1-111112-1-1−2i2i−2i2i−2i−2i2i2i-111-12-2-1-111002-2ii−i−i0000−2i2iiiii−i−i−i−i-1-11122-1-1-1-1-2-211110000000000−2i2i0000ii−i−i0000
χ562-22-2-1222-2-2-2-111-222-2-1-111-1-1211-2-2-1-11122-2-2-1-111112-1-1−2i2i−2i2i−2i−2i2i2i-111-12-2-1-11100-22ii−i−i0000−2i2iiiii−i−i−i−i11-1-1-2-2111122-1-1-1-100000000002i−2i0000−i−iii0000
χ572-22-2-122-22-2-2-111-222-211-1-1-1-1211-2-2-1-1112-22211-1-1-1-1-2112i−2i−2i2i2i2i−2i−2i-111-1-2211-1-10000−iii−i0000−2i2i−i−iiiii−i−i3−3−330033−3−300−3−3330000000000000000i3−i3−i3i30000
χ582-22-2-122-22-2-2-111-222-211-1-1-1-1211-2-2-1-1112-22211-1-1-1-1-2112i−2i−2i2i2i2i−2i−2i-111-1-2211-1-10000−iii−i0000−2i2i−i−iiiii−i−i−333−300−3−3330033−3−30000000000000000−i3i3i3−i30000
χ592-22-2-122-22-2-2-111-222-211-1-1-1-1211-2-2-1-1112-22211-1-1-1-1-211−2i2i2i−2i−2i−2i2i2i-111-1-2211-1-10000i−i−ii00002i−2iii−i−i−i−iii3−3−330033−3−300−3−3330000000000000000−i3i3i3−i30000
χ602-22-2-122-22-2-2-111-222-211-1-1-1-1211-2-2-1-1112-22211-1-1-1-1-211−2i2i2i−2i−2i−2i2i2i-111-1-2211-1-10000i−i−ii00002i−2iii−i−i−i−iii−333−300−3−3330033−3−30000000000000000i3−i3−i3i30000
χ61444444-2-4-4-2-244444-24-4-4-4-44-2-2-2-2-2-24-244-2-4-42-4-4-4-42222200000000-2-2-2-222222200000000000000000000000000000000000000000000000000000000000000
χ6244444-2-244-2-2444-2-2-2-24444-2-21-2-211-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-200000000111111111144000000-2-2-2-200000000000000000000000000-2-21111000000000000000000
χ6344444-2-244-2-2444-2-2-2-24444-2-21-2-211-2-2-2-21-2-2-2-2-2-2-2-2-2-2-2-2000000001111111111-4-400000022220000000000000000000000000022-1-1-1-1000000000000000000
χ6444444-2-2-4-4-2-2444-2-2-2-2-4-4-4-4-2-21-2-211-2-2-2-21222222222222000000001111-1-1-1-1-1-100000000−2i32i3−2i32i30000000000000000000000000000i3−i3i3−i3000000000000000000
χ6544444-2-2-4-4-2-2444-2-2-2-2-4-4-4-4-2-21-2-211-2-2-2-21222222222222000000001111-1-1-1-1-1-1000000002i3−2i32i3−2i30000000000000000000000000000−i3i3−i3i3000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.