Finite Group Databasebeta

← Group #13155708

Character table — Group #13155708

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818181824242424242424242424242436363636363672727272108108
order1222333446666666663336666666661212121212121212121236661212121212121212444488121212121212121224242424242424242424242424242424444412121212121212121212121212121212444412121212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-111
χ51111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-11111
χ71111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91-11-1111-11-1-1-111-1-1-11111-1-1-1-1-111-1111-1111-1-1-1-11-1-111-11-111-1-1i−i1-1i−i11-1-1ii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−iii−i−ii−i1-1ii−i−i11-1-11-1i−ii−ii−i1-11-1
χ101-11-1111-11-1-1-111-1-1-11111-1-1-1-1-111-1111-1111-1-1-1-11-1-111-11-111-1-1i−i1-1−ii11-1-1ii−i−i−i−i−i−i−i−i−i−iiiiiiiiii−ii−iii−i−ii−i1-1ii−i−i11-1-1-11−iii−i−ii-11-11
χ111-11-1111-11-1-1-111-1-1-11111-1-1-1-1-111-1111-1111-1-1-1-11-1-111-11-111-1-1i−i-11i−i-1-111ii−i−iiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−i−iiii−i-11ii−i−i-1-1111-1−ii−ii−ii1-1-11
χ121-11-1111-11-1-1-111-1-1-11111-1-1-1-1-111-1111-1111-1-1-1-11-1-111-11-111-1-1i−i-11−ii-1-111ii−i−i−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−iiii−i-11ii−i−i-1-111-11i−i−iii−i-111-1
χ131-11-1111-11-1-1-111-1-1-11111-1-1-1-1-111-1111-1111-1-1-1-11-1-111-11-111-1-1−ii1-1i−i11-1-1−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−i−iii−ii1-1−i−iii11-1-1-11i−i−iii−i-11-11
χ141-11-1111-11-1-1-111-1-1-11111-1-1-1-1-111-1111-1111-1-1-1-11-1-111-11-111-1-1−ii1-1−ii11-1-1−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−iii−ii1-1−i−iii11-1-11-1−ii−ii−ii1-11-1
χ151-11-1111-11-1-1-111-1-1-11111-1-1-1-1-111-1111-1111-1-1-1-11-1-111-11-111-1-1−ii-11i−i-1-111−i−iiiiiiiiiii−i−i−i−i−i−i−i−ii−ii−iii−i−i−ii-11−i−iii-1-111-11−iii−i−ii-111-1
χ161-11-1111-11-1-1-111-1-1-11111-1-1-1-1-111-1111-1111-1-1-1-11-1-111-11-111-1-1−ii-11−ii-1-111−i−iii−i−i−i−i−i−i−i−iiiiiiiiii−ii−iii−i−i−ii-11−i−iii-1-1111-1i−ii−ii−i1-1-11
χ172222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000022-2-2-2-2-2-2000000000000000022000000
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χ21222222-1222222-1-1-1222-1-122-1-1-12-1-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-22200-1-1-1-111110000000000000000-2-2-2-21111-2-2221111-1-1-1-1000011000000
χ22222222-1222222-1-1-1222-1-122-1-1-12-1-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2001111111100000000000000002222-1-1-1-1-2-2-2-2111111110000-1-1000000
χ23222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000−i3i3−i3i3−i3i3−i3i3000000000000000022-2-211110000−i3i3−i3i3−i3i3−i3i30000-1-1000000
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χ25222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000i3−i3i3−i3−i3i3−i3i30000000000000000-2-222-1-1-1-10000−i3i3−i3i3i3−i3i3−i3000011000000
χ26222222-1-2-22222-1-1-1222-1-122-1-1-12-1-1-1-211-2-2-2-2-2-2-2-1-1-1-111111111000000i3−i3i3−i3i3−i3i3−i3000000000000000022-2-211110000i3−i3i3−i3i3−i3i3−i30000-1-1000000
χ2722222-12222-12-1222-12-12-1-1-12-1-1-122-1-1222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-10022222222000022-1-1-1-1-1-122-1-1-1-1-1-10000000000-1-10000-1-1-1-1002200-1-10000
χ2822222-12222-12-1222-12-12-1-1-12-1-1-122-1-1222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-10022-2-222220000-2-2111111-2-21111110000000000-1-10000-1-1-1-100-2-200110000
χ2922222-12222-12-1222-12-12-1-1-12-1-1-122-1-1222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-100-2-222-2-2-2-2000022-1-1-1-1-1-122-1-1-1-1-1-10000000000110000111100-2-200110000
χ3022222-12222-12-1222-12-12-1-1-12-1-1-122-1-1222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-100-2-2-2-2-2-2-2-20000-2-2111111-2-211111100000000001100001111002200-1-10000
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χ322222-12222-12-122222-1-1-12-1-1-122-1-1-12222-1-1-12-1-1-1-1-1-1-1-1-122-1-1-1-12200-2-20000222211-2-2111111-2-2111100000000-1-100-1-1-1-10000-2-20000001100
χ332222-12222-12-122222-1-1-12-1-1-122-1-1-12222-1-1-12-1-1-1-1-1-1-1-1-122-1-1-1-1-2-200220000-2-2-2-2-1-122-1-1-1-1-1-122-1-1-1-100000000110011110000-2-20000001100
χ342222-12222-12-122222-1-1-12-1-1-122-1-1-12222-1-1-12-1-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2-20000-2-2-2-211-2-2111111-2-211110000000011001111000022000000-1-100
χ352-22-22222-2-2-2-222-2-2-22222-2-2-2-2-222-22-2-22-2-2-222222-2-22-22-22-2-2220000000000000000000000000000002i−2i−2i2i−2i−2i2i2i00000000000000002i−2i000000
χ362-22-22222-2-2-2-222-2-2-22222-2-2-2-2-222-22-2-22-2-2-222222-2-22-22-22-2-222000000000000000000000000000000−2i2i2i−2i2i2i−2i−2i0000000000000000−2i2i000000
χ372-22-222-12-2-2-2-22-111-222-1-1-2-21112-11-1-21-1-2-2-22222-111-11-11-111-1-1000000−i3i3i3−i33−3−3300000000000000002i−2i−2i2iii−i−i00003−3−33−i3i3i3−i30000−ii000000
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χ392-22-222-12-2-2-2-22-111-222-1-1-2-21112-11-1-21-1-2-2-22222-111-11-11-111-1-1000000i3−i3−i3i33−3−330000000000000000−2i2i2i−2i−i−iii00003−3−33i3−i3−i3i30000i−i000000
χ402-22-222-12-2-2-2-22-111-222-1-1-2-21112-11-1-21-1-2-2-22222-111-11-11-111-1-1000000i3−i3−i3i3−333−300000000000000002i−2i−2i2iii−i−i0000−333−3i3−i3−i3i30000−ii000000
χ412-22-222-1-22-2-2-22-111-222-1-1-2-21112-11-12-11222-2-2-2-2-111-1-11-11-1-1112i−2i2-200-1-111−i−iii00000000000000002i−2i2i−2i−i−iii2i−2i2-2−i−iii-1-1110000−ii000000
χ422-22-222-1-22-2-2-22-111-222-1-1-2-21112-11-12-11222-2-2-2-2-111-1-11-11-1-1112i−2i-220011-1-1−i−iii0000000000000000−2i2i−2i2iii−i−i2i−2i-22−i−iii11-1-10000i−i000000
χ432-22-222-1-22-2-2-22-111-222-1-1-2-21112-11-12-11222-2-2-2-2-111-1-11-11-1-111−2i2i2-200-1-111ii−i−i0000000000000000−2i2i−2i2iii−i−i−2i2i2-2ii−i−i-1-1110000i−i000000
χ442-22-222-1-22-2-2-22-111-222-1-1-2-21112-11-12-11222-2-2-2-2-111-1-11-11-1-111−2i2i-220011-1-1ii−i−i00000000000000002i−2i2i−2i−i−iii−2i2i-22ii−i−i11-1-10000−ii000000
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χ472-22-22-12-22-21-2-12-2-212-12-111-211-12-2-1-12-22-1-11-211-111-12-2-11-1-11100-222i−2i-2-22200002i2i−i−i−i−i−i−i−2i−2iiiiiii00000000001-1000011-1-100−2i2i00i−i0000
χ482-22-22-12-22-21-2-12-2-212-12-111-211-12-2-1-12-22-1-11-211-111-12-2-11-1-11100-22−2i2i-2-2220000−2i−2iiiiiii2i2i−i−i−i−i−i−i00000000001-1000011-1-1002i−2i00−ii0000
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χ974-4-44-24400-2-42-4-44-442-2-242-2-2-44222-40000000000-22-220000000000000000000000i6−i600i6−i6−i6i6−i6i600−i6i6i6−i600000000000000000000000000000000
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χ994-4-44-2-2400-2222-44-4-221-2-2-11-22-2-122200003i−3i00−3i3i1-11-100003i−3i−3i3i00000000000000i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000000000000000000000000000
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χ1014-4-44-2-2400-2222-44-4-221-2-2-11-22-2-12220000−3i3i003i−3i1-11-10000−3i3i3i−3i00000000000000i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.