Finite Group Databasebeta

← Group #13140031

Character table — Group #13140031

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111222222222222222222226666666666666666121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order122244442234466666661212121212121212336666661212121212121212366666666666121212121212121212121212888888882424242424242424242424242424242424446688881212121212122424242424242424
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
χ511111111-1-11-1-111-1-1-1-1111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1111111-1-1-1-1
χ611111111-1-11-1-111-1-1-1-1111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1111111-1-1-1-1-1-11111
χ711111111-1-11-1-111-1-1-1-1111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1111-1-111-1-1-1-111-1-1-1-11111
χ811111111-1-11-1-111-1-1-1-1111-1-1-1-11111111111111111111-1-1-1-111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-111-1-1-111-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i11-1-111i−ii−i11-1-1-1-1ii−i−iii−i−i
χ101111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-1-111-1-1−ii−ii-1-11111−i−iii−i−iii
χ111111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii11-1-111−ii−ii11-1-1-1-1−i−iii−i−iii
χ121111-1-1-1-1111-1-11111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-1-111-1-1i−ii−i-1-11111ii−i−iii−i−i
χ131111-1-1-1-1-1-111111-1-1-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-11-111i−i−ii-1-111-1-1ii−i−i−i−iii
χ141111-1-1-1-1-1-111111-1-1-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11-11-1-1−iii−i11-1-111−i−iiiii−i−i
χ151111-1-1-1-1-1-111111-1-1-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-111−iii−i-1-111-1-1−i−iiiii−i−i
χ161111-1-1-1-1-1-111111-1-1-1-11-1-11111-1-111111111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-111111-1-1-1-11111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-11-1-1i−i−ii11-1-111ii−i−i−i−iii
χ1722222222222222222222222222222-1222-1-1-1-1-1-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-10000000000000000000000002222-1-10000-1-1-1-1-1-100000000
χ1822222222222222222222222222222-1222-1-1-1-1-1-1-12222-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-1-1000000000000000000000000-2-2-2-211000011111100000000
χ192222222222222222222222222222-12-1-1-12222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000000000000000000000000002222000000-1-1-1-1-1-1-1-1
χ202222222222222222222222222222-12-1-1-12222222-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000000000000000000000000-2-2-2-200000011111111
χ2122222222-2-22-2-222-2-2-2-2222-2-2-2-2222-1222-1-1-1-1-1-1-12222-1-2-211-1-11111-1-2-211-1-1-1-111110000000000000000000000002-2-22-1-100001111-1-100000000
χ2222222222-2-22-2-222-2-2-2-2222-2-2-2-2222-1222-1-1-1-1-1-1-12222-1-2-211-1-11111-1-2-211-1-1-1-11111000000000000000000000000-222-2110000-1-1-1-11100000000
χ2322222222-2-22-2-222-2-2-2-2222-2-2-2-222-12-1-1-12222222-1-1-1-1-111-2-2-1-11111-111-2-2-1-1-1-1111100000000000000000000000000000022-2-2000000-1-1-1-11111
χ2422222222-2-22-2-222-2-2-2-2222-2-2-2-222-12-1-1-12222222-1-1-1-1-111-2-2-1-11111-111-2-2-1-1-1-11111000000000000000000000000000000-2-2220000001111-1-1-1-1
χ252222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-22-1222-1-1-11111-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-2111111111100000000000000000000000022-2-2-1-10000-1-1111100000000
χ262222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-22-1222-1-1-11111-2-2-2-2-122-1-1-1-1-1-1-1-1-1-2-21111111111000000000000000000000000-2-22211000011-1-1-1-100000000
χ272222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-12-1-1-1222-2-2-2-21111-1-1-122-1-1-1-1-1-1-111-2-2111111110000000000000000000000000000002i−2i2i−2i000000−i−iii−i−iii
χ282222-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2-12-1-1-1222-2-2-2-21111-1-1-122-1-1-1-1-1-1-111-2-211111111000000000000000000000000000000−2i2i−2i2i000000ii−i−iii−i−i
χ292222-2-2-2-2-2-222222-2-2-2-22-2-22222-2-22-1222-1-1-11111-2-2-2-2-1-2-211-1-11111-122-1-11111-1-1-1-10000000000000000000000002-22-2-1-1000011-1-11100000000
χ302222-2-2-2-2-2-222222-2-2-2-22-2-22222-2-22-1222-1-1-11111-2-2-2-2-1-2-211-1-11111-122-1-11111-1-1-1-1000000000000000000000000-22-22110000-1-111-1-100000000
χ312222-2-2-2-2-2-222222-2-2-2-22-2-22222-2-2-12-1-1-1222-2-2-2-21111-111-2-2-1-11111-1-1-1221111-1-1-1-10000000000000000000000000000002i−2i−2i2i000000−i−iiiii−i−i
χ322222-2-2-2-2-2-222222-2-2-2-22-2-22222-2-2-12-1-1-1222-2-2-2-21111-111-2-2-1-11111-1-1-1221111-1-1-1-1000000000000000000000000000000−2i2i2i−2i000000ii−i−i−i−iii
χ3322-2-22i−2i2i−2i002002-20000-22i−2i00002i−2i222-2-22-2-22i2i−2i−2i2i2i−2i−2i200002-20000-200002i2i−2i−2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300002ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ23−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ1300000000000000000000000000000000
χ3422-2-22i−2i2i−2i002002-20000-22i−2i00002i−2i222-2-22-2-22i2i−2i−2i2i2i−2i−2i200002-20000-200002i2i−2i−2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ232ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ3522-2-2−2i2i−2i2i002002-20000-2−2i2i0000−2i2i222-2-22-2-2−2i−2i2i2i−2i−2i2i2i200002-20000-20000−2i−2i2i2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000−2ζ5−2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ5+2ζ132ζ7+2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ7−2ζ2300000000000000000000000000000000
χ3622-2-2−2i2i−2i2i002002-20000-2−2i2i0000−2i2i222-2-22-2-2−2i−2i2i2i−2i−2i2i2i200002-20000-20000−2i−2i2i2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ2300000000000000000000000000000000
χ372-22-22i−2i−2i2i2-222i−2i-2222-2-2-22i−2i2i2i−2i−2i−2i2i22-22-2-22-22i−2i2i−2i2i−2i2i−2i22-22-2-2222-2-2-22i−2i2i−2i2i−2i2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ382-22-22i−2i−2i2i2-222i−2i-2222-2-2-22i−2i2i2i−2i−2i−2i2i2-1-22-21-11−ii−ii2i−2i2i−2i-12-2-111-1-1-11112i−2i−ii−ii−ii−i−iii0000000000000000000000000000−i3i30000−i3i33−33−300000000
χ392-22-22i−2i−2i2i2-222i−2i-2222-2-2-22i−2i2i2i−2i−2i−2i2i2-1-22-21-11−ii−ii2i−2i2i−2i-12-2-111-1-1-11112i−2i−ii−ii−ii−i−iii0000000000000000000000000000i3−i30000i3−i3−33−3300000000
χ402-22-22i−2i−2i2i2-222i−2i-2222-2-2-22i−2i2i2i−2i−2i−2i2i-121-11-22-22i−2i2i−2i−ii−ii-1-112-21-1-1-1111−ii2i−2i−ii−ii−i−iii0000000000000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
χ412-22-22i−2i−2i2i2-222i−2i-2222-2-2-22i−2i2i2i−2i−2i−2i2i-121-11-22-22i−2i2i−2i−ii−ii-1-112-21-1-1-1111−ii2i−2i−ii−ii−i−iii0000000000000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ422-22-22i−2i−2i2i-222−2i2i-22-2-222-22i−2i−2i−2i2i2i−2i2i22-22-2-22-22i−2i2i−2i2i−2i2i−2i2-22-22-22-2-222-2−2i2i−2i2i2i−2i2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ432-22-22i−2i−2i2i-222−2i2i-22-2-222-22i−2i−2i−2i2i2i−2i2i2-1-22-21-11−ii−ii2i−2i2i−2i-1-221-11-111-1-11−2i2ii−i−ii−iiii−i−i0000000000000000000000000000−i3i30000i3−i3−333−300000000
χ442-22-22i−2i−2i2i-222−2i2i-22-2-222-22i−2i−2i−2i2i2i−2i2i2-1-22-21-11−ii−ii2i−2i2i−2i-1-221-11-111-1-11−2i2ii−i−ii−iiii−i−i0000000000000000000000000000i3−i30000−i3i33−3−3300000000
χ452-22-22i−2i−2i2i-222−2i2i-22-2-222-22i−2i−2i−2i2i2i−2i2i-121-11-22-22i−2i2i−2i−ii−ii-11-1-221-111-1-11i−i−2i2i−ii−iiii−i−i0000000000000000000000000000000000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ462-22-22i−2i−2i2i-222−2i2i-22-2-222-22i−2i−2i−2i2i2i−2i2i-121-11-22-22i−2i2i−2i−ii−ii-11-1-221-111-1-11i−i−2i2i−ii−iiii−i−i0000000000000000000000000000000000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
χ472-22-2−2i2i2i−2i2-22−2i2i-2222-2-2-2−2i2i−2i−2i2i2i2i−2i22-22-2-22-2−2i2i−2i2i−2i2i−2i2i22-22-2-2222-2-2-2−2i2i−2i2i−2i2i−2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000
χ482-22-2−2i2i2i−2i2-22−2i2i-2222-2-2-2−2i2i−2i−2i2i2i2i−2i2-1-22-21-11i−ii−i−2i2i−2i2i-12-2-111-1-1-1111−2i2ii−ii−ii−iii−i−i0000000000000000000000000000−i3i30000−i3i3−33−3300000000
χ492-22-2−2i2i2i−2i2-22−2i2i-2222-2-2-2−2i2i−2i−2i2i2i2i−2i2-1-22-21-11i−ii−i−2i2i−2i2i-12-2-111-1-1-1111−2i2ii−ii−ii−iii−i−i0000000000000000000000000000i3−i30000i3−i33−33−300000000
χ502-22-2−2i2i2i−2i2-22−2i2i-2222-2-2-2−2i2i−2i−2i2i2i2i−2i-121-11-22-2−2i2i−2i2ii−ii−i-1-112-21-1-1-1111i−i−2i2ii−ii−iii−i−i0000000000000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ512-22-2−2i2i2i−2i2-22−2i2i-2222-2-2-2−2i2i−2i−2i2i2i2i−2i-121-11-22-2−2i2i−2i2ii−ii−i-1-112-21-1-1-1111i−i−2i2ii−ii−iii−i−i0000000000000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ522-22-2−2i2i2i−2i-2222i−2i-22-2-222-2−2i2i2i2i−2i−2i2i−2i22-22-2-22-2−2i2i−2i2i−2i2i−2i2i2-22-22-22-2-222-22i−2i2i−2i−2i2i−2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000
χ532-22-2−2i2i2i−2i-2222i−2i-22-2-222-2−2i2i2i2i−2i−2i2i−2i2-1-22-21-11i−ii−i−2i2i−2i2i-1-221-11-111-1-112i−2i−iii−ii−i−i−iii0000000000000000000000000000−i3i30000i3−i33−3−3300000000
χ542-22-2−2i2i2i−2i-2222i−2i-22-2-222-2−2i2i2i2i−2i−2i2i−2i2-1-22-21-11i−ii−i−2i2i−2i2i-1-221-11-111-1-112i−2i−iii−ii−i−i−iii0000000000000000000000000000i3−i30000−i3i3−333−300000000
χ552-22-2−2i2i2i−2i-2222i−2i-22-2-222-2−2i2i2i2i−2i−2i2i−2i-121-11-22-2−2i2i−2i2ii−ii−i-11-1-221-111-1-11−ii2i−2ii−ii−i−i−iii0000000000000000000000000000000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ562-22-2−2i2i2i−2i-2222i−2i-22-2-222-2−2i2i2i2i−2i−2i2i−2i-121-11-22-2−2i2i−2i2ii−ii−i-11-1-221-111-1-11−ii2i−2ii−ii−i−i−iii0000000000000000000000000000000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ572-2-2222-2-200200-2-200002220000-2-222-2-22-2-222-2-222-2-2220000-2-20000200002-2-22000000002i−2i2i−2i000000002i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ582-2-2222-2-200200-2-200002220000-2-222-2-22-2-222-2-222-2-2220000-2-20000200002-2-2200000000−2i2i−2i2i00000000−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ592-2-22-2-22200200-2-200002-2-200002222-2-22-2-22-222-2-222-220000-2-2000020000-222-2000000002-2-220000000022-2-2-2-222000000000000000000000000
χ602-2-22-2-22200200-2-200002-2-200002222-2-22-2-22-222-2-222-220000-2-2000020000-222-200000000-222-200000000-2-22222-2-2000000000000000000000000
χ614444444444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-211111111000000000000000000000000000000000000000000000000
χ6244444444-4-44-4-444-4-4-4-4444-4-4-4-444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-1122221111-1-1-1-1000000000000000000000000000000000000000000000000
χ634444-4-4-4-4444-4-44444444-4-4-4-4-4-4-4-4-2-2-2-2-2-2-2-2222222221-2-2-2-211111112222-1-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000
χ644444-4-4-4-4-4-444444-4-4-4-44-4-44444-4-4-2-2-2-2-2-2-2-2222222221222211-1-1-1-11-2-2-2-2-1-1-1-11111000000000000000000000000000000000000000000000000
χ6544-4-44i−4i4i−4i004004-40000-44i−4i00004i−4i4-24-4-4-222−2i−2i2i2i4i4i−4i−4i-20000-22000020000−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ6644-4-44i−4i4i−4i004004-40000-44i−4i00004i−4i-24-2224-4-44i4i−4i−4i−2i−2i2i2i-20000-22000020000−2i−2i2i2i0000000000000000000000000000000000000000000000000000
χ6744-4-44i−4i4i−4i004004-40000-44i−4i00004i−4i-2-2-222-222−2i−2i2i2i−2i−2i2i2i100001-13-33-3-10000ii−i−i3i−3i3i−3i000000000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.