Finite Group Databasebeta

← Group #13140033

Character table — Group #13140033

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111122222222222244446666666666666666666666661212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order122244442234466612121212661212336666666666121212121212121212121212366666666612121212121212121212888888882424242424242424242424242424242424446688881212121212122424242424242424
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
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111
χ511111111-1-11-1-11111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111111-1-111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1111111-1-1-1-1
χ611111111-1-11-1-11111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111111-1-111-1-1-1-11-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-11111
χ711111111-1-11-1-11111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111111-1-111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-111-1-1-1-111-1-1-1-11111
χ811111111-1-11-1-11111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111111-1-111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-111-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-1111-1-1111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111i−ii−i11-1-1-1-1ii−i−iii−i−i
χ101111-1-1-1-1111-1-1111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111-1-1−ii−ii-1-11111−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−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111−ii−ii11-1-1-1-1−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−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1i−ii−i-1-11111ii−i−iii−i−i
χ131111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-11-1-111-1-1-1-1111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-11-111i−i−ii-1-111-1-1ii−i−i−i−iii
χ141111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-11-1-111-1-1-1-1111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11-11-1-1−iii−i11-1-111−i−iiiii−i−i
χ151111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-11-1-111-1-1-1-1111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-111−iii−i-1-111-1-1−i−iiiii−i−i
χ161111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-1-1-1-1-11-1-111-1-1-1-1111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-11-1-1i−i−ii11-1-111ii−i−i−i−iii
χ172222222222222222222222222-12222222-1-1-1222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000002222-1-10000-1-1-1-1-1-100000000
χ182222222222222222222222222-12222222-1-1-1222222-1-1-1-122-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2-211000011111100000000
χ19222222222222222222222222-12-1-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ20222222222222222222222222-12-1-1-1-1-1-1-1222-1-1-1-1-1-12222-1-1-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111000000000000000000000000
χ2122222222-2-22-2-22222222-2-2-2-22-122-2-2-2-22-1-1-122-2-2-2-2-1-1-1-122-111-1-11111-111-1-1-1-111110000000000000000000000002-2-22-1-100001111-1-100000000
χ2222222222-2-22-2-22222222-2-2-2-22-122-2-2-2-22-1-1-122-2-2-2-2-1-1-1-122-111-1-11111-111-1-1-1-11111000000000000000000000000-222-2110000-1-1-1-11100000000
χ2322222222-2-22-2-22222222-2-2-2-2-12-1-11111-1222-1-111112222-1-1-1-2-2-1-11111-1-2-2-1-1-1-111112222-2-2-2-2-1-1-1-1-1-1-1-111111111000000000000000000000000
χ2422222222-2-22-2-22222222-2-2-2-2-12-1-11111-1222-1-111112222-1-1-1-2-2-1-11111-1-2-2-1-1-1-11111-2-2-2-2222211111111-1-1-1-1-1-1-1-1000000000000000000000000
χ252222-2-2-2-2222-2-2222-2-2-2-222-2-22-12222222-1-1-1-2-2-2-2-2-21111-2-2-1-1-1-1-1-1-1-1-1-1111111111100000000000000000000000022-2-2-1-10000-1-1111100000000
χ262222-2-2-2-2222-2-2222-2-2-2-222-2-22-12222222-1-1-1-2-2-2-2-2-21111-2-2-1-1-1-1-1-1-1-1-1-11111111111000000000000000000000000-2-22211000011-1-1-1-100000000
χ272222-2-2-2-2222-2-2222-2-2-2-222-2-2-12-1-1-1-1-1-1-1222111111-2-2-2-211-122-1-1-1-1-1-1-1-2-2111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii000000000000000000000000
χ282222-2-2-2-2222-2-2222-2-2-2-222-2-2-12-1-1-1-1-1-1-1222111111-2-2-2-211-122-1-1-1-1-1-1-1-2-211111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i000000000000000000000000
χ292222-2-2-2-2-2-2222222-2-2-2-2-2-2222-122-2-2-2-22-1-1-1-2-222221111-2-2-111-1-11111-1-1-11111-1-1-1-10000000000000000000000002-22-2-1-1000011-1-11100000000
χ302222-2-2-2-2-2-2222222-2-2-2-2-2-2222-122-2-2-2-22-1-1-1-2-222221111-2-2-111-1-11111-1-1-11111-1-1-1-1000000000000000000000000-22-22110000-1-111-1-100000000
χ312222-2-2-2-2-2-2222222-2-2-2-2-2-222-12-1-11111-122211-1-1-1-1-2-2-2-211-1-2-2-1-11111-1221111-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i000000000000000000000000
χ322222-2-2-2-2-2-2222222-2-2-2-2-2-222-12-1-11111-122211-1-1-1-1-2-2-2-211-1-2-2-1-11111-1221111-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii000000000000000000000000
χ3322-2-22i−2i2i−2i002002-2-22i2i−2i−2i0000222-20000-22-2-22i−2i00002i2i−2i−2i2i−2i2002-20000-2002i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300000000000000000000000000000000
χ3422-2-22i−2i2i−2i002002-2-22i2i−2i−2i0000222-20000-22-2-22i−2i00002i2i−2i−2i2i−2i2002-20000-2002i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ3522-2-22i−2i2i−2i002002-2-22i2i−2i−2i0000-12-11−i3−i3i3i312-2-2−ii33−3−32i2i−2i−2i−ii-100-11−i3−i3i3i3100−i−iii33−3−32ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13000000000000000000000000
χ3622-2-22i−2i2i−2i002002-2-22i2i−2i−2i0000-12-11−i3−i3i3i312-2-2−ii33−3−32i2i−2i−2i−ii-100-11−i3−i3i3i3100−i−iii33−3−3−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13000000000000000000000000
χ3722-2-22i−2i2i−2i002002-2-22i2i−2i−2i0000-12-11i3i3−i3−i312-2-2−ii−3−3332i2i−2i−2i−ii-100-11i3i3−i3−i3100−i−iii−3−3332ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13000000000000000000000000
χ3822-2-22i−2i2i−2i002002-2-22i2i−2i−2i0000-12-11i3i3−i3−i312-2-2−ii−3−3332i2i−2i−2i−ii-100-11i3i3−i3−i3100−i−iii−3−333−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13000000000000000000000000
χ3922-2-2−2i2i−2i2i002002-2-2−2i−2i2i2i0000222-20000-22-2-2−2i2i0000−2i−2i2i2i−2i2i2002-20000-200−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ4022-2-2−2i2i−2i2i002002-2-2−2i−2i2i2i0000222-20000-22-2-2−2i2i0000−2i−2i2i2i−2i2i2002-20000-200−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000000000000000000000000000
χ4122-2-2−2i2i−2i2i002002-2-2−2i−2i2i2i0000-12-11−i3−i3i3i312-2-2i−i−3−333−2i−2i2i2ii−i-100-11−i3−i3i3i3100ii−i−i−3−333−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23000000000000000000000000
χ4222-2-2−2i2i−2i2i002002-2-2−2i−2i2i2i0000-12-11−i3−i3i3i312-2-2i−i−3−333−2i−2i2i2ii−i-100-11−i3−i3i3i3100ii−i−i−3−3332ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23000000000000000000000000
χ4322-2-2−2i2i−2i2i002002-2-2−2i−2i2i2i0000-12-11i3i3−i3−i312-2-2i−i33−3−3−2i−2i2i2ii−i-100-11i3i3−i3−i3100ii−i−i33−3−3−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23ζ5−ζ13ζ5−ζ13−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23ζ7−ζ23ζ7−ζ23000000000000000000000000
χ4422-2-2−2i2i−2i2i002002-2-2−2i−2i2i2i0000-12-11i3i3−i3−i312-2-2i−i33−3−3−2i−2i2i2ii−i-100-11i3i3−i3−i3100ii−i−i33−3−32ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23−ζ5+ζ13−ζ5+ζ13ζ5−ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23−ζ7+ζ23−ζ7+ζ23000000000000000000000000
χ452-22-22i−2i−2i2i2-222i−2i-22-22i−2i2i−2i2-22i−2i22-222-22-2-2-22-22i−2i2i−2i2i−2i2i−2i2i−2i−2i2i22-2-222-22-2-22i−2i2i−2i2i−2i2i−2i2i−2i000000000000000000000000000000000000000000000000
χ462-22-22i−2i−2i2i2-222i−2i-22-22i−2i2i−2i2-22i−2i2-1-222-22-2-21-112i−2i2i−2i2i−2i−ii−ii−2i2i-1-111-1-11-111−ii−ii−ii−ii−ii0000000000000000000000000000−i3i30000−i3i33−33−300000000
χ472-22-22i−2i−2i2i2-222i−2i-22-22i−2i2i−2i2-22i−2i2-1-222-22-2-21-112i−2i2i−2i2i−2i−ii−ii−2i2i-1-111-1-11-111−ii−ii−ii−ii−ii0000000000000000000000000000i3−i30000i3−i3−33−3300000000
χ482-22-22i−2i−2i2i2-222i−2i-22-22i−2i2i−2i2-22i−2i-121-1-11-111-22-2−ii−ii−ii2i−2i2i−2ii−i-12-21-1-11-1112i−2i−ii−ii−ii−ii00000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ492-22-22i−2i−2i2i2-222i−2i-22-22i−2i2i−2i2-22i−2i-121-1-11-111-22-2−ii−ii−ii2i−2i2i−2ii−i-12-21-1-11-1112i−2i−ii−ii−ii−ii00000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ502-22-22i−2i−2i2i-222−2i2i-22-22i−2i2i−2i-22−2i2i22-22-22-22-2-22-22i−2i−2i2i−2i2i2i−2i2i−2i−2i2i2-22-22-22-22-2−2i2i2i−2i2i−2i−2i2i−2i2i000000000000000000000000000000000000000000000000
χ512-22-22i−2i−2i2i-222−2i2i-22-22i−2i2i−2i-22−2i2i2-1-22-22-22-21-112i−2i−2i2i−2i2i−ii−ii−2i2i-11-11-11-11-11i−i−ii−iii−ii−i0000000000000000000000000000−i3i30000i3−i3−333−300000000
χ522-22-22i−2i−2i2i-222−2i2i-22-22i−2i2i−2i-22−2i2i2-1-22-22-22-21-112i−2i−2i2i−2i2i−ii−ii−2i2i-11-11-11-11-11i−i−ii−iii−ii−i0000000000000000000000000000i3−i30000−i3i33−3−3300000000
χ532-22-22i−2i−2i2i-222−2i2i-22-22i−2i2i−2i-22−2i2i-121-11-11-11-22-2−iii−ii−i2i−2i2i−2ii−i-1-221-11-11-11−2i2i−ii−iii−ii−i00000000ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23000000000000000000000000
χ542-22-22i−2i−2i2i-222−2i2i-22-22i−2i2i−2i-22−2i2i-121-11-11-11-22-2−iii−ii−i2i−2i2i−2ii−i-1-221-11-11-11−2i2i−ii−iii−ii−i00000000−ζ5+ζ13ζ5−ζ13−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ7+ζ23ζ7−ζ23000000000000000000000000
χ552-22-2−2i2i2i−2i2-22−2i2i-22-2−2i2i−2i2i2-2−2i2i22-222-22-2-2-22-2−2i2i−2i2i−2i2i−2i2i−2i2i2i−2i22-2-222-22-2-2−2i2i−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.