Finite Group Databasebeta

← Group #13140030

Character table — Group #13140030

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111122222222222244446666666666666666666666661212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order122244442234466612121212661212336666666666121212121212121212121212366666666612121212121212121212222244446666666612121212121212128888888824242424242424242424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ511111111-1-11-1-11111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ611111111-1-11-1-11111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111
χ711111111-1-11-1-11111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ811111111-1-11-1-11111111-1-1-1-1111111-1-1-1-1111111-1-1-1-111111-1-111-1-1-1-11-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1i−ii−ii−ii−iii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-1111-1-1111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−ii−ii−ii−ii−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-1111-1-1111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111i−ii−i−ii−iiii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-1111-1-1111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111−ii−iii−ii−i−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111i−i−iii−i−iiii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-11111−iii−i−iii−i−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1111-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1i−i−ii−iii−iii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-1-1-1111111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1111-1-1-1-11111-1-11111-1-1-1-1-1-111111111-1-1-1-1−iii−ii−i−ii−i−iiiii−i−iii−i−i−i−iii
χ172222222222222222222222222-122-1-1-1-1-1-12-1-1-1-1-1-1-1-1-12222-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ182222222222222222222222222-122-1-1-1-1-1-12-1-1-1-1-1-1-1-1-12222-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ19222222222222222222222222-12-1-1222222-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000222200000000-1-1-1-1-1-1-1-1
χ20222222222222222222222222-12-1-1222222-1222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000000000-2-2-2-20000000011111111
χ2122222222-2-22-2-22222222-2-2-2-22-122-1-111112-1-1-1-1-111112222-1-2-2-1-11111-1-2-2-1-1-1-1111122-2-222-2-2-1-1-1-11111-1-1-1-11111000000000000000000000000
χ2222222222-2-22-2-22222222-2-2-2-22-122-1-111112-1-1-1-1-111112222-1-2-2-1-11111-1-2-2-1-1-1-11111-2-222-2-2221111-1-1-1-11111-1-1-1-1000000000000000000000000
χ2322222222-2-22-2-22222222-2-2-2-2-12-1-122-2-2-2-2-122222-2-2-2-2-1-1-1-1-111-1-11111-111-1-1-1-11111000000000000000000000000000022-2-200000000-1-1-1-11111
χ2422222222-2-22-2-22222222-2-2-2-2-12-1-122-2-2-2-2-122222-2-2-2-2-1-1-1-1-111-1-11111-111-1-1-1-111110000000000000000000000000000-2-222000000001111-1-1-1-1
χ252222-2-2-2-2222-2-2222-2-2-2-222-2-22-122-1-1-1-1-1-12-111111111-2-2-2-2-122-1-1-1-1-1-1-1-2-2111111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ262222-2-2-2-2222-2-2222-2-2-2-222-2-22-122-1-1-1-1-1-12-111111111-2-2-2-2-122-1-1-1-1-1-1-1-2-211111111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ272222-2-2-2-2222-2-2222-2-2-2-222-2-2-12-1-1222222-12-2-2-2-2-2-2-2-21111-1-1-1-1-1-1-1-1-1-1111111111100000000000000000000000000002i−2i2i−2i00000000−i−iii−i−iii
χ282222-2-2-2-2222-2-2222-2-2-2-222-2-2-12-1-1222222-12-2-2-2-2-2-2-2-21111-1-1-1-1-1-1-1-1-1-111111111110000000000000000000000000000−2i2i−2i2i00000000ii−i−iii−i−i
χ292222-2-2-2-2-2-2222222-2-2-2-2-2-2222-122-1-111112-11111-1-1-1-1-2-2-2-2-1-2-2-1-11111-1221111-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-1000000000000000000000000
χ302222-2-2-2-2-2-2222222-2-2-2-2-2-2222-122-1-111112-11111-1-1-1-1-2-2-2-2-1-2-2-1-11111-1221111-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-11111000000000000000000000000
χ312222-2-2-2-2-2-2222222-2-2-2-2-2-222-12-1-122-2-2-2-2-12-2-2-2-222221111-111-1-11111-1-1-11111-1-1-1-100000000000000000000000000002i−2i−2i2i00000000−i−iiiii−i−i
χ322222-2-2-2-2-2-2222222-2-2-2-2-2-222-12-1-122-2-2-2-2-12-2-2-2-222221111-111-1-11111-1-1-11111-1-1-1-10000000000000000000000000000−2i2i2i−2i00000000ii−i−i−i−iii
χ3322-2-22i2i−2i−2i002002-2-22i2i−2i−2i0000222-22-20000-2-22i2i−2i−2i00002i2i−2i−2i2002-20000-2002i2i−2i−2i0000002-2002i−2i000022-2-200002i2i−2i−2i000000000000000000000000
χ3422-2-22i2i−2i−2i002002-2-22i2i−2i−2i0000222-22-20000-2-22i2i−2i−2i00002i2i−2i−2i2002-20000-2002i2i−2i−2i000000-2200−2i2i0000-2-2220000−2i−2i2i2i000000000000000000000000
χ3522-2-22i2i−2i−2i002002-2-22i2i−2i−2i00002-12-2-11−i3−i3i3i3-21−i−iii33−3−32i2i−2i−2i-100-11−i3−i3i3i3100−i−iii33−3−3002-2002i−2i−i3−i3i3i3-1-11133−3−3−i−iii000000000000000000000000
χ3622-2-22i2i−2i−2i002002-2-22i2i−2i−2i00002-12-2-11−i3−i3i3i3-21−i−iii33−3−32i2i−2i−2i-100-11−i3−i3i3i3100−i−iii33−3−300-2200−2i2ii3i3−i3−i311-1-1−3−333ii−i−i000000000000000000000000
χ3722-2-22i2i−2i−2i002002-2-22i2i−2i−2i00002-12-2-11i3i3−i3−i3-21−i−iii−3−3332i2i−2i−2i-100-11i3i3−i3−i3100−i−iii−3−333002-2002i−2ii3i3−i3−i3-1-111−3−333−i−iii000000000000000000000000
χ3822-2-22i2i−2i−2i002002-2-22i2i−2i−2i00002-12-2-11i3i3−i3−i3-21−i−iii−3−3332i2i−2i−2i-100-11i3i3−i3−i3100−i−iii−3−33300-2200−2i2i−i3−i3i3i311-1-133−3−3ii−i−i000000000000000000000000
χ3922-2-2−2i−2i2i2i002002-2-2−2i−2i2i2i0000222-22-20000-2-2−2i−2i2i2i0000−2i−2i2i2i2002-20000-200−2i−2i2i2i0000002-200−2i2i000022-2-20000−2i−2i2i2i000000000000000000000000
χ4022-2-2−2i−2i2i2i002002-2-2−2i−2i2i2i0000222-22-20000-2-2−2i−2i2i2i0000−2i−2i2i2i2002-20000-200−2i−2i2i2i000000-22002i−2i0000-2-22200002i2i−2i−2i000000000000000000000000
χ4122-2-2−2i−2i2i2i002002-2-2−2i−2i2i2i00002-12-2-11−i3−i3i3i3-21ii−i−i−3−333−2i−2i2i2i-100-11−i3−i3i3i3100ii−i−i−3−333002-200−2i2i−i3−i3i3i3-1-111−3−333ii−i−i000000000000000000000000
χ4222-2-2−2i−2i2i2i002002-2-2−2i−2i2i2i00002-12-2-11−i3−i3i3i3-21ii−i−i−3−333−2i−2i2i2i-100-11−i3−i3i3i3100ii−i−i−3−33300-22002i−2ii3i3−i3−i311-1-133−3−3−i−iii000000000000000000000000
χ4322-2-2−2i−2i2i2i002002-2-2−2i−2i2i2i00002-12-2-11i3i3−i3−i3-21ii−i−i33−3−3−2i−2i2i2i-100-11i3i3−i3−i3100ii−i−i33−3−3002-200−2i2ii3i3−i3−i3-1-11133−3−3ii−i−i000000000000000000000000
χ4422-2-2−2i−2i2i2i002002-2-2−2i−2i2i2i00002-12-2-11i3i3−i3−i3-21ii−i−i33−3−3−2i−2i2i2i-100-11i3i3−i3−i3100ii−i−i33−3−300-22002i−2i−i3−i3i3i311-1-1−3−333−i−iii000000000000000000000000
χ452-22-22i−2i2i−2i2-222i−2i-22-22i−2i2i−2i2-22i−2i22-22-222-22-2-2-22i−2i2i−2i2i−2i2i−2i2i−2i2i−2i22-2-222-22-2-22i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ462-22-22i−2i2i−2i2-222i−2i-22-22i−2i2i−2i2-22i−2i2-1-221-1-11-11-21−ii−ii−ii−ii2i−2i2i−2i-12-21-1-11-1112i−2i−ii−ii−ii−ii00000000−i3i3−i3i3−i3i3−i3i33−33−33−33−3000000000000000000000000
χ472-22-22i−2i2i−2i2-222i−2i-22-22i−2i2i−2i2-22i−2i2-1-221-1-11-11-21−ii−ii−ii−ii2i−2i2i−2i-12-21-1-11-1112i−2i−ii−ii−ii−ii00000000i3−i3i3−i3i3−i3i3−i3−33−33−33−33000000000000000000000000
χ482-22-22i−2i2i−2i2-222i−2i-22-22i−2i2i−2i2-22i−2i-121-1-222-22-21-22i−2i2i−2i2i−2i2i−2i−ii−ii-1-111-1-11-111−ii−ii−ii−ii−ii0000000000000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ492-22-22i−2i2i−2i2-222i−2i-22-22i−2i2i−2i2-22i−2i-121-1-222-22-21-22i−2i2i−2i2i−2i2i−2i−ii−ii-1-111-1-11-111−ii−ii−ii−ii−ii0000000000000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ502-22-22i−2i2i−2i-222−2i2i-22-22i−2i2i−2i-22−2i2i22-22-22-22-22-2-22i−2i2i−2i−2i2i−2i2i2i−2i2i−2i2-22-22-22-22-2−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ512-22-22i−2i2i−2i-222−2i2i-22-22i−2i2i−2i-22−2i2i2-1-221-11-11-1-21−ii−iii−ii−i2i−2i2i−2i-1-221-11-11-11−2i2i−ii−iii−ii−i00000000−i3i3−i3i3i3−i3i3−i33−33−3−33−33000000000000000000000000
χ522-22-22i−2i2i−2i-222−2i2i-22-22i−2i2i−2i-22−2i2i2-1-221-11-11-1-21−ii−iii−ii−i2i−2i2i−2i-1-221-11-11-11−2i2i−ii−iii−ii−i00000000i3−i3i3−i3−i3i3−i3i3−33−333−33−3000000000000000000000000
χ532-22-22i−2i2i−2i-222−2i2i-22-22i−2i2i−2i-22−2i2i-121-1-22-22-221-22i−2i2i−2i−2i2i−2i2i−ii−ii-11-11-11-11-11i−i−ii−iii−ii−i0000000000000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ542-22-22i−2i2i−2i-222−2i2i-22-22i−2i2i−2i-22−2i2i-121-1-22-22-221-22i−2i2i−2i−2i2i−2i2i−ii−ii-11-11-11-11-11i−i−ii−iii−ii−i0000000000000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ552-22-2−2i2i−2i2i2-22−2i2i-22-2−2i2i−2i2i2-2−2i2i22-22-222-22-2-2-2−2i2i−2i2i−2i2i−2i2i−2i2i−2i2i22-2-222-22-2-2−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ562-22-2−2i2i−2i2i2-22−2i2i-22-2−2i2i−2i2i2-2−2i2i2-1-221-1-11-11-21i−ii−ii−ii−i−2i2i−2i2i-12-21-1-11-111−2i2ii−ii−ii−ii−i00000000−i3i3−i3i3−i3i3−i3i3−33−33−33−33000000000000000000000000
χ572-22-2−2i2i−2i2i2-22−2i2i-22-2−2i2i−2i2i2-2−2i2i2-1-221-1-11-11-21i−ii−ii−ii−i−2i2i−2i2i-12-21-1-11-111−2i2ii−ii−ii−ii−i00000000i3−i3i3−i3i3−i3i3−i33−33−33−33−3000000000000000000000000
χ582-22-2−2i2i−2i2i2-22−2i2i-22-2−2i2i−2i2i2-2−2i2i-121-1-222-22-21-2−2i2i−2i2i−2i2i−2i2ii−ii−i-1-111-1-11-111i−ii−ii−ii−ii−i0000000000000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
χ592-22-2−2i2i−2i2i2-22−2i2i-22-2−2i2i−2i2i2-2−2i2i-121-1-222-22-21-2−2i2i−2i2i−2i2i−2i2ii−ii−i-1-111-1-11-111i−ii−ii−ii−ii−i0000000000000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ602-22-2−2i2i−2i2i-2222i−2i-22-2−2i2i−2i2i-222i−2i22-22-22-22-22-2-2−2i2i−2i2i2i−2i2i−2i−2i2i−2i2i2-22-22-22-22-22i−2i−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ612-22-2−2i2i−2i2i-2222i−2i-22-2−2i2i−2i2i-222i−2i2-1-221-11-11-1-21i−ii−i−ii−ii−2i2i−2i2i-1-221-11-11-112i−2ii−ii−i−ii−ii00000000−i3i3−i3i3i3−i3i3−i3−33−333−33−3000000000000000000000000
χ622-22-2−2i2i−2i2i-2222i−2i-22-2−2i2i−2i2i-222i−2i2-1-221-11-11-1-21i−ii−i−ii−ii−2i2i−2i2i-1-221-11-11-112i−2ii−ii−i−ii−ii00000000i3−i3i3−i3−i3i3−i3i33−33−3−33−33000000000000000000000000
χ632-22-2−2i2i−2i2i-2222i−2i-22-2−2i2i−2i2i-222i−2i-121-1-22-22-221-2−2i2i−2i2i2i−2i2i−2ii−ii−i-11-11-11-11-11−iii−ii−i−ii−ii0000000000000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ642-22-2−2i2i−2i2i-2222i−2i-22-2−2i2i−2i2i-222i−2i-121-1-22-22-221-2−2i2i−2i2i2i−2i2i−2ii−ii−i-11-11-11-11-11−iii−ii−i−ii−ii0000000000000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.