Finite Group Databasebeta

← Group #13155725

Character table — Group #13155725

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181818182424242424242424363636363636363672727272108108
order12223334466666666612121212333666666666121212121212121212121212366612121212121244888824242424242424242424242424242424242424242424242424242424242424244444121212121212121222441212121266121222
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-111
χ511111111111111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1
χ911-1-11111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-11-1-111-111-1-1i−ii−i1-1ii−i−i11-1-1iiiiii−i−i−i−i−i−i111111-1-1-1-1-1-1i−ii−iii−i−iii−i−i1-1i−iii−i−i1-1i−i1-1
χ1011-1-11111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-11-1-111-111-1-1i−ii−i-11ii−i−i-1-111iiiiii−i−i−i−i−i−i-1-1-1-1-1-1111111−ii−iiii−i−iii−i−i1-1−ii−i−iii1-1−ii-11
χ1111-1-11111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-11-1-111-111-1-1i−i−ii1-1−i−iii11-1-1−i−i−i−i−i−iiiiiii111111-1-1-1-1-1-1−ii−iiii−i−iii−i−i-11i−i−i−iii-11i−i-11
χ1211-1-11111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-11-1-111-111-1-1i−i−ii-11−i−iii-1-111−i−i−i−i−i−iiiiiii-1-1-1-1-1-1111111i−ii−iii−i−iii−i−i-11−iiii−i−i-11−ii1-1
χ1311-1-11111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-11-1-111-111-1-1−iii−i1-1ii−i−i11-1-1iiiiii−i−i−i−i−i−i111111-1-1-1-1-1-1i−ii−i−i−iii−i−iii-11−iiii−i−i-11−ii-11
χ1411-1-11111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-11-1-111-111-1-1−iii−i-11ii−i−i-1-111iiiiii−i−i−i−i−i−i-1-1-1-1-1-1111111−ii−ii−i−iii−i−iii-11i−i−i−iii-11i−i1-1
χ1511-1-11111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-11-1-111-111-1-1−ii−ii1-1−i−iii11-1-1−i−i−i−i−i−iiiiiii111111-1-1-1-1-1-1−ii−ii−i−iii−i−iii1-1−ii−i−iii1-1−ii1-1
χ1611-1-11111-1-1111-1-1-1-1-111-1-1111-1-1-1-1-1111-11-111-1-11-111-1-11-1-111-111-1-1−ii−ii-11−i−iii-1-111−i−i−i−i−i−iiiiiii-1-1-1-1-1-1111111i−ii−i−i−iii−i−iii1-1i−iii−i−i1-1i−i-11
χ172222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000000000000000000000000022-2-20000000000002-22-2000000
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χ20222222-122-122-12-122222222-1-122-1-1-12-1-1-1-12-1-1222-122-1-1-1-1-1-1-1-1-1-1-1-122-2-200-2-2-2-2000011111111111100000000000000002-12-1-1-1-1-1-2-2000000110000
χ21222222-122-122-12-122222222-1-122-1-1-12-1-1-1-12-1-1222-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-21-211111-2-2000000110000
χ22222222-122-122-12-122222222-1-122-1-1-12-1-1-1-12-1-1222-122-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-200001111111111110000000000000000-21-21111122000000-1-10000
χ2322222-122222-1222-1-12-1-1-1-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1002222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-122-1-1-1-12222000000000000-1-1-1-1000000
χ2422222-122222-1222-1-12-1-1-1-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10022-2-2-1-1-1-1111122-1-1-1-122-1-1-1-1-2-21111-2-21111-2-2-2-20000000000001111000000
χ2522222-122222-1222-1-12-1-1-1-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2221111-1-1-1-1-2-21111-2-2111122-1-1-1-122-1-1-1-1-2-2-2-20000000000001111000000
χ2622222-122222-1222-1-12-1-1-1-1-12-1-1-12-1-1-12-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-211111111-2-21111-2-21111-2-21111-2-211112222000000000000-1-1-1-1000000
χ2722222-12-2-222-1222-1-121111-12-1-1-12-1-1-12-12-2-21111-2-21111-1-1-1-1-2-211110000003−33−33−33−30033−3−30033−3−30033−3−30033−3−322-2-2000000000000-11-11000000
χ2822222-12-2-222-1222-1-121111-12-1-1-12-1-1-12-12-2-21111-2-21111-1-1-1-1-2-211110000003−33−3−33−330033−3−30033−3−300−3−33300−3−333-2-2220000000000001-11-1000000
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χ3022222-12-2-222-1222-1-121111-12-1-1-12-1-1-12-12-2-21111-2-21111-1-1-1-1-2-21111000000−33−33−33−3300−3−33300−3−33300−3−33300−3−33322-2-2000000000000-11-11000000
χ312222-122222-122-1222-12222-1-12-1-1-122-1-12-12-122-1-1-12-1-122-1-1-1-1-1-1-1-1-1-122002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-10000-12-12-1-1-1-10022000000-1-100
χ322222-122222-122-1222-12222-1-12-1-1-122-1-12-12-122-1-1-12-1-122-1-1-1-1-1-1-1-1-1-12200-2-20000-2-2-2-20000000000001111111111110000-12-12-1-1-1-100-2-20000001100
χ332222-122222-122-1222-12222-1-12-1-1-122-1-12-12-122-1-1-12-1-122-1-1-1-1-1-1-1-1-1-1-2-2002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100001-21-2111100-2-20000001100
χ342222-122222-122-1222-12222-1-12-1-1-122-1-12-12-122-1-1-12-1-122-1-1-1-1-1-1-1-1-1-1-2-200-2-20000-2-2-2-200000000000011111111111100001-21-211110022000000-1-100
χ3522-2-2222-22-2222-2-2-2-2-2-2-222222-2-2-2-2-2222-2-22-2-222-22-2-2222-2-22-22-2-222000000000000000000000000000000000000002i−2i−2i2i0000000000002i−2i−2i2i000000
χ3622-2-2222-22-2222-2-2-2-2-2-2-222222-2-2-2-2-2222-2-22-2-222-22-2-2222-2-22-22-2-22200000000000000000000000000000000000000−2i2i2i−2i000000000000−2i2i2i−2i000000
χ3722-2-222-12-2122-1-21-2-2-222-2-22-1-1-2-21112-1-11-1-2-1-1-2-2212211-111-1-11-1-1112i−2i2i−2i002i2i−2i−2i0000−i−i−i−i−i−iiiiiii00000000000000002i−i−2ii−i−iii2-2000000-110000
χ3822-2-222-12-2122-1-21-2-2-222-2-22-1-1-2-21112-1-11-1-2-1-1-2-2212211-111-1-11-1-1112i−2i−2i2i00−2i−2i2i2i0000iiiiii−i−i−i−i−i−i00000000000000002i−i−2ii−i−iii-220000001-10000
χ3922-2-222-12-2122-1-21-2-2-222-2-22-1-1-2-21112-1-11-1-2-1-1-2-2212211-111-1-11-1-111−2i2i2i−2i002i2i−2i−2i0000−i−i−i−i−i−iiiiiii0000000000000000−2ii2i−iii−i−i-220000001-10000
χ4022-2-222-12-2122-1-21-2-2-222-2-22-1-1-2-21112-1-11-1-2-1-1-2-2212211-111-1-11-1-111−2i2i−2i2i00−2i−2i2i2i0000iiiiii−i−i−i−i−i−i0000000000000000−2ii2i−iii−i−i2-2000000-110000
χ4122-2-22-122-2-22-12-2-211-2-1-111-12-111-211-12-1-22-2-1-1112-2-1-111-111-12-2-1-111002i−2i2-2−i−iii-1-1112i2i−i−i−i−i−2i−2iiiii22-1-1-1-1-2-211112i−2i2i−2i000000000000−i−iii000000
χ4222-2-22-122-2-22-12-2-211-2-1-111-12-111-211-12-1-22-2-1-1112-2-1-111-111-12-2-1-111002i−2i-22−i−iii11-1-12i2i−i−i−i−i−2i−2iiiii-2-2111122-1-1-1-1−2i2i−2i2i000000000000ii−i−i000000
χ4322-2-22-122-2-22-12-2-211-2-1-111-12-111-211-12-1-22-2-1-1112-2-1-111-111-12-2-1-11100−2i2i2-2ii−i−i-1-111−2i−2iiiii2i2i−i−i−i−i22-1-1-1-1-2-21111−2i2i−2i2i000000000000ii−i−i000000
χ4422-2-22-122-2-22-12-2-211-2-1-111-12-111-211-12-1-22-2-1-1112-2-1-111-111-12-2-1-11100−2i2i-22ii−i−i11-1-1−2i−2iiiii2i2i−i−i−i−i-2-2111122-1-1-1-12i−2i2i−2i000000000000−i−iii000000
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χ4622-2-22-12-22-22-12-2-211-211-1-1-12-111-211-12-1-2-2211-1-1-2211-1-1-111-1-2211-1-1000000−i3i3i3−i3−333−300−i3−i3i3i300i3i3−i3−i300−3−3330033−3−32i−2i−2i2i000000000000−iii−i000000
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χ7344-4-4-24-24-42-24-222-4-4244-4-4-21-222-122-21-2-1-22-2-222-22-2-2221-1-111-111-1-14i−4i0000000000000000000000000000000000000000−2i−2i2i2iii−i−i00000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.