Finite Group Databasebeta

← Group #13138784

Character table — Group #13138784

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111222222222222222222226666666666666666121212121212121212121212121212121212121212121212181818181818181818181818181818181818181818181818363636363636363636363636363636363636363636363636
order1222444436668888121212122424242424242424336666661212121212121212366612121212242424242424242424242424242424244444888812121212121212122424242424242424224466668888121212122424242424242424
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
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-11111
χ5111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ6111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ7111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111-11-111-1-1-1-11111-1-1-1-1-1-11111
χ8111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-11-1-11111-1-1-1-1111111-1-1-1-1
χ91111-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i11-1-11111i−ii−i-1-1-1-1ii−i−iii−i−i
χ101111-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111-1-1-1-1−ii−ii1111−i−iii−i−iii
χ111111-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-1-1111-1-1i−i−ii-1-111ii−i−i−i−iii
χ121111-1-1-1-11111ii−i−i-1-1-1-1iiii−i−i−i−i11111111-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-111-1-1-111−iii−i11-1-1−i−iiiii−i−i
χ131111-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii11-1-11111−ii−ii-1-1-1-1−i−iii−i−iii
χ141111-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-1-111-1-1-1-1i−ii−i1111ii−i−iii−i−i
χ151111-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-1-1111-1-1−iii−i-1-111−i−iiiii−i−i
χ161111-1-1-1-11111−i−iii-1-1-1-1−i−i−i−iiiii11111111-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-111-1-1-111i−i−ii11-1-1ii−i−i−i−iii
χ1722222222222222222222222222222-122-1-12-122-1-122-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-1000000000000000000000000020200-1-1002200-1-10000-1-1-1-1
χ1822222222222222222222222222222-122-1-12-122-1-122-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1-1-10000000000000000000000000-20-2001100-2-2001100001111
χ192222222222222222222222222222-12-1-122-12-1-122-1-122-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-10000000000000000000000002020-1-1002200-1-100-1-1-1-10000
χ202222222222222222222222222222-12-1-122-12-1-122-1-122-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-1000000000000000000000000-20-201100-2-200110011110000
χ21222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-122-1-12-122-1-122-1-1-1-1-1-1-1-1-1-1-2-211-2-21111111111000000000000000000000000020200-1-100-2-200-1-100001111
χ22222222222222-2-2-2-22222-2-2-2-2-2-2-2-22-122-1-12-122-1-122-1-1-1-1-1-1-1-1-1-1-2-211-2-211111111110000000000000000000000000-20-20011002200110000-1-1-1-1
χ23222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-122-12-1-122-1-122-1-1-1-1-1-1-1-111-2-211-2-2111111110000000000000000000000002020-1-100-2-200-1-10011110000
χ24222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-12-1-122-12-1-122-1-122-1-1-1-1-1-1-1-111-2-211-2-211111111000000000000000000000000-20-20110022001100-1-1-1-10000
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χ262222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i2-122-1-12-1-2-211-2-211-1-1-1-111112i2i−i−i−2i−2iii−i−i−i−iiiii0000000000000000000000000-202001100−2i2i00-1-10000ii−i−i
χ272222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i-12-1-122-1211-2-211-2-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii00000000000000000000000020-20-1-1002i−2i001100−i−iii0000
χ282222-2-2-2-222222i2i−2i−2i-2-2-2-22i2i2i2i−2i−2i−2i−2i-12-1-122-1211-2-211-2-2-1-1-1-11111−i−i2i2iii−2i−2i−i−i−i−iiiii000000000000000000000000-20201100−2i2i00-1-100ii−i−i0000
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χ302222-2-2-2-22222−2i−2i2i2i-2-2-2-2−2i−2i−2i−2i2i2i2i2i2-122-1-12-1-2-211-2-211-1-1-1-11111−2i−2iii2i2i−i−iiiii−i−i−i−i0000000000000000000000000-2020011002i−2i00-1-10000−i−iii
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χ3422-2-22i−2i2i−2i2-22-200002i−2i2i−2i00000000222-22-2-2-22i−2i2i−2i2i−2i2i−2i22-2-22i−2i2i−2i000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000002ζ5+2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ5−2ζ13−2ζ7−2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ7+2ζ23000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.