Finite Group Databasebeta

← Group #13155690

Character table — Group #13155690

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818181824242424242424242424242436363636363672727272108108
order122233344666666666333666666666121212121212121212123666121212121212121222446666881212121224242424242424242424242424242424444412121212666666121212121212444412121212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111-1-111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
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
χ91-11-1111-11-1-111-1-1-1-11111-1-1-1-1-1111-111-1111-1-1-1-11-1-1111-1-111-1-11-1i−i11-1-1i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−ii−ii−iii−i−i1-111-1-1i−iii−i−i1-1i−ii−ii−i1-11-1
χ101-11-1111-11-1-111-1-1-1-11111-1-1-1-1-1111-111-1111-1-1-1-11-1-1111-1-111-1-11-1i−i11-1-1−iiii−i−i−i−i−i−i−i−i−i−iiiiiiiiii−ii−iii−i−i1-111-1-1i−iii−i−i-11−iii−i−ii-11-11
χ111-11-1111-11-1-111-1-1-1-11111-1-1-1-1-1111-111-1111-1-1-1-11-1-1111-1-111-1-11-1−ii11-1-1i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−i−iii1-111-1-1−ii−i−iii-11i−i−iii−i-11-11
χ121-11-1111-11-1-111-1-1-1-11111-1-1-1-1-1111-111-1111-1-1-1-11-1-1111-1-111-1-11-1−ii11-1-1−ii−i−iii−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−iii1-111-1-1−ii−i−iii1-1−ii−ii−ii1-11-1
χ131-11-1111-11-1-111-1-1-1-11111-1-1-1-1-1111-111-1111-1-1-1-11-1-1111-1-111-1-1-11i−i-1-111i−iii−i−iiiiiiiii−i−i−i−i−i−i−i−i−ii−ii−i−iii-11-1-111i−iii−i−i1-1−ii−ii−ii1-1-11
χ141-11-1111-11-1-111-1-1-1-11111-1-1-1-1-1111-111-1111-1-1-1-11-1-1111-1-111-1-1-11i−i-1-111−iiii−i−i−i−i−i−i−i−i−i−iiiiiiiii−ii−ii−i−iii-11-1-111i−iii−i−i-11i−i−iii−i-111-1
χ151-11-1111-11-1-111-1-1-1-11111-1-1-1-1-1111-111-1111-1-1-1-11-1-1111-1-111-1-1-11−ii-1-111i−i−i−iiiiiiiiiii−i−i−i−i−i−i−i−ii−ii−iii−i−i-11-1-111−ii−i−iii-11−iii−i−ii-111-1
χ161-11-1111-11-1-111-1-1-1-11111-1-1-1-1-1111-111-1111-1-1-1-11-1-1111-1-111-1-1-11−ii-1-111−ii−i−iii−i−i−i−i−i−i−i−iiiiiiiiii−ii−iii−i−i-11-1-111−ii−i−iii1-1i−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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χ20222222-122222-12-1-1222-1-122-1-1-12-1-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-1-1-1-10011110000000000000000-2-2-2-2111122-1-1-1-1-2-21111000011000000
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χ22222222-122222-12-1-1222-1-122-1-1-12-1-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111100111100000000000000002222-1-1-1-1-2-21111-2-211110000-1-1000000
χ23222222-1-2-2222-12-1-1222-1-122-1-1-12-1-1-1-211-2-2-2-2-2-2-2-1-1-1-1111111110000−i3i3−i3i300−i3i3−i3i3000000000000000022-2-2111100−i3i3−i3i300−i3i3−i3i30000-1-1000000
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χ25222222-1-2-2222-12-1-1222-1-122-1-1-12-1-1-1-211-2-2-2-2-2-2-2-1-1-1-1111111110000i3−i3i3−i300−i3i3−i3i30000000000000000-2-222-1-1-1-100i3−i3i3−i300−i3i3−i3i3000011000000
χ26222222-1-2-2222-12-1-1222-1-122-1-1-12-1-1-1-211-2-2-2-2-2-2-2-1-1-1-1111111110000i3−i3i3−i300i3−i3i3−i3000000000000000022-2-2111100i3−i3i3−i300i3−i3i3−i30000-1-1000000
χ2722222-12222-1-12222-12-12-1-1-12-1-1-12-12-1222-1-1-12-1-1-1-1-1-12-12-1-1-1-1-12200222222000022-1-1-1-1-1-122-1-1-1-1-1-100000000-1-1-1-1-1-1000000002200-1-10000
χ2822222-12222-1-12222-12-12-1-1-12-1-1-12-12-1222-1-1-12-1-1-1-1-1-12-12-1-1-1-1-122002222-2-20000-2-2111111-2-211111100000000-1-1-1-1-1-100000000-2-200110000
χ2922222-12222-1-12222-12-12-1-1-12-1-1-12-12-1222-1-1-12-1-1-1-1-1-12-12-1-1-1-1-1-2-200-2-2-2-222000022-1-1-1-1-1-122-1-1-1-1-1-10000000011111100000000-2-200110000
χ3022222-12222-1-12222-12-12-1-1-12-1-1-12-12-1222-1-1-12-1-1-1-1-1-12-12-1-1-1-1-1-2-200-2-2-2-2-2-20000-2-2111111-2-211111100000000111111000000002200-1-10000
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χ322222-12222-1222-1222-1-1-12-1-1-122-1-12-1222-1-1-12-1-1-1-1-1-1-1-12-12-1-1-1-100220000-2-2222211-2-2111111-2-2111100000000000000-1-1-1-1-1-1-2-20000001100
χ332222-12222-1222-1222-1-1-12-1-1-122-1-12-1222-1-1-12-1-1-1-1-1-1-1-12-12-1-1-1-100-2-2000022-2-2-2-2-1-122-1-1-1-1-1-122-1-1-1-100000000000000111111-2-20000001100
χ342222-12222-1222-1222-1-1-12-1-1-122-1-12-1222-1-1-12-1-1-1-1-1-1-1-12-12-1-1-1-100-2-20000-2-2-2-2-2-211-2-2111111-2-211110000000000000011111122000000-1-100
χ352-22-22222-2-2-222-2-2-2-22222-2-2-2-2-2222-2-2-22-2-2-222222-2-22-2-222-2-2220000000000000000000000000000002i−2i−2i2i−2i−2i2i2i00000000000000002i−2i000000
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χ372-22-222-12-2-2-22-1-211-222-1-1-2-21112-1-11-21-1-2-2-22222-111-111-1-111-1-10000−i3i3i3−i3003−3−3300000000000000002i−2i−2i2iii−i−i00−i3i3i3−i3003−3−330000−ii000000
χ382-22-222-12-2-2-22-1-211-222-1-1-2-21112-1-11-21-1-2-2-22222-111-111-1-111-1-10000−i3i3i3−i300−333−30000000000000000−2i2i2i−2i−i−iii00−i3i3i3−i300−333−30000i−i000000
χ392-22-222-12-2-2-22-1-211-222-1-1-2-21112-1-11-21-1-2-2-22222-111-111-1-111-1-10000i3−i3−i3i3003−3−330000000000000000−2i2i2i−2i−i−iii00i3−i3−i3i3003−3−330000i−i000000
χ402-22-222-12-2-2-22-1-211-222-1-1-2-21112-1-11-21-1-2-2-22222-111-111-1-111-1-10000i3−i3−i3i300−333−300000000000000002i−2i−2i2iii−i−i00i3−i3−i3i300−333−30000−ii000000
χ412-22-222-1-22-2-22-1-211-222-1-1-2-21112-1-112-11222-2-2-2-2-111-1-1-111-1-1112-22i−2i-1-11100−i−iii00000000000000002i−2i2i−2i−i−iii2-2-1-1112i−2i−i−iii0000−ii000000
χ422-22-222-1-22-2-22-1-211-222-1-1-2-21112-1-112-11222-2-2-2-2-111-1-1-111-1-1112-2−2i2i-1-11100ii−i−i0000000000000000−2i2i−2i2iii−i−i2-2-1-111−2i2iii−i−i0000i−i000000
χ432-22-222-1-22-2-22-1-211-222-1-1-2-21112-1-112-11222-2-2-2-2-111-1-1-111-1-111-222i−2i11-1-100−i−iii0000000000000000−2i2i−2i2iii−i−i-2211-1-12i−2i−i−iii0000i−i000000
χ442-22-222-1-22-2-22-1-211-222-1-1-2-21112-1-112-11222-2-2-2-2-111-1-1-111-1-111-22−2i2i11-1-100ii−i−i00000000000000002i−2i2i−2i−i−iii-2211-1-1−2i2iii−i−i0000−ii000000
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χ472-22-22-12-22-21-12-2-2-212-12-111-211-12-1-2-12-22-1-11-211-111-12-1-21-1-111-2200-2-2222i−2i00002i2i−i−i−i−i−i−i−2i−2iiiiiii000000001-111-1-100000000−2i2i00i−i0000
χ482-22-22-12-22-21-12-2-2-212-12-111-211-12-1-2-12-22-1-11-211-111-12-1-21-1-111-2200-2-222−2i2i0000−2i−2iiiiiii2i2i−i−i−i−i−i−i000000001-111-1-1000000002i−2i00−ii0000
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χ954-4-444-2400-422-44-44-2-4-24-22-2-42-22-4240000000000-22-22000000000000000000000000i6−i6i6−i6i6−i600−i6i6−i6i6−i6i600000000000000000000000000000000
χ964-4-444-2400-422-44-44-2-4-24-22-2-42-22-4240000000000-22-22000000000000000000000000−i6i6−i6i6−i6i600i6−i6i6−i6i6−i600000000000000000000000000000000
χ974-4-44-244002-4-4-4-2-4442-2-242-22-4422-4-20000000000-22-2200000000000000000000006−6006−6−66−6600−666−600000000000000000000000000000000
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χ994-4-44-2-2400222-4-2-44-221-2-2-1122-2-122-200003i−3i00−3i3i1-11-100003i−3i−3i3i000000000000006−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ1300000000000000000000000000000000
χ1004-4-44-2-2400222-4-2-44-221-2-2-1122-2-122-200003i−3i00−3i3i1-11-100003i−3i−3i3i00000000000000−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ1300000000000000000000000000000000
χ1014-4-44-2-2400222-4-2-44-221-2-2-1122-2-122-20000−3i3i003i−3i1-11-10000−3i3i3i−3i000000000000006−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ2300000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.