Finite Group Databasebeta

← Group #13155878

Character table — Group #13155878

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818242424242424242424242424363636727272727272108108
order1222333446666666663336666666661212121212121212121236661212121212121212224466668812121212242424242424242424242424242424244412121212666666121212121212266441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-111-1-111
χ51111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-111-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-11111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1
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χ11222222-122222-1-12-1222-1-122-1-1-1-12-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100-1-1-1-1000000000000000022-1-1-1-122-1-1-1-122-1-1-1-12-1-100000000
χ12222222-122222-1-12-1222-1-122-1-1-1-12-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-1-1-1-10011110000000000000000-2-2111122-1-1-1-1-2-21111-21100000000
χ13222222-122222-1-12-1222-1-122-1-1-1-12-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-222111100-1-1-1-10000000000000000-2-21111-2-2111122-1-1-1-1-21100000000
χ14222222-122222-1-12-1222-1-122-1-1-1-12-1-12-1-12222222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111001111000000000000000022-1-1-1-1-2-21111-2-211112-1-100000000
χ15222222-1-2-2222-1-12-1222-1-122-1-1-1-12-1-1-211-2-2-2-2-2-2-2-1-1-1-1111111110000−i3−i3i3i300−i3−i3i3i3000000000000000022-1-1-1-100−i3−i3i3i300−i3−i3i3i3-21100000000
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χ17222222-1-2-2222-1-12-1222-1-122-1-1-1-12-1-1-211-2-2-2-2-2-2-2-1-1-1-1111111110000i3i3−i3−i300−i3−i3i3i30000000000000000-2-2111100i3i3−i3−i300−i3−i3i3i32-1-100000000
χ18222222-1-2-2222-1-12-1222-1-122-1-1-1-12-1-1-211-2-2-2-2-2-2-2-1-1-1-1111111110000i3i3−i3−i300i3i3−i3−i3000000000000000022-1-1-1-100i3i3−i3−i300i3i3−i3−i3-21100000000
χ1922222-12222-1-122222-1-12-1-1-122-1-1-1-12222-1-1-12-1-1-1-1-1-1-1-1-122-1-1-1-1220022222200002222-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-10000000000200-1-100
χ2022222-12222-1-122222-1-12-1-1-122-1-1-1-12222-1-1-12-1-1-1-1-1-1-1-1-122-1-1-1-122002222-2-20000-2-2-2-2111111111111000000-1-1-1-1-1-10000000000-2001100
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χ252222-12222-12222-12-12-1-12-1-1-1-122-12-1-1222-1-1-12-1-1-1-1-1-122-1-1-1-1-1-100-2-2000022-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-1000000000000111111000-20110000
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χ272-22-222200-22-22-2-2-22-22222-22-22-2-2-2-2000000000022-2-20000000000000000−i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i22i−2i2i2i−2i−2i0000000000000000000002−2
χ282-22-222200-22-22-2-2-22-22222-22-22-2-2-2-2000000000022-2-20000000000000000−i2i20000−i2−i2i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2i2i2−2i2i−2i−2i2i2i000000000000000000000−22
χ292-22-222200-22-22-2-2-22-22222-22-22-2-2-2-2000000000022-2-20000000000000000i2−i20000i2i2−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2−i2−i22i−2i2i2i−2i−2i000000000000000000000−22
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χ844-44-4-2-24002-224-42-4-221-2-21-1-22-22-1220000−3i3i003i−3i11-1-100003i−3i−3i3i00000000−2i22i20000i2i2−i2−i2i2i2−i2−i2ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ23−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ2300000000000000000000000000000
χ854-44-4-2-24002-224-42-4-221-2-21-1-22-22-1220000−3i3i003i−3i11-1-100003i−3i−3i3i000000002i2−2i20000−i2−i2i2i2−i2−i2i2i2−ζ5+2ζ7−ζ13+2ζ232ζ5−ζ7+2ζ13−ζ232ζ5−ζ7+2ζ13−ζ23−ζ5+2ζ7−ζ13+2ζ23ζ5−2ζ7+ζ13−2ζ23−2ζ5+ζ7−2ζ13+ζ23−2ζ5+ζ7−2ζ13+ζ23ζ5−2ζ7+ζ13−2ζ2300000000000000000000000000000
χ864-4-444-24-44-422-4-444-4-2-24-222-4-422-2-244-44-2-2-2-4222-222-22-2-4422-2-200000000000000000000000000000000000000000000000000000000000
χ874-4-444-2-24-4-422224-2-4-2-2-212222-1-1-21-2-4-222224-2-2-21-1-111-1-2211-1-14-400-22-220000000000000000000000000000-221-11-100000000000000000
χ884-4-444-2-24-4-422224-2-4-2-2-212222-1-1-21-2-4-222224-2-2-21-1-111-1-2211-1-1-44002-22-200000000000000000000000000002-2-11-1100000000000000000
χ894-4-444-2-2-44-422224-2-4-2-2-212222-1-1-21-242-2-2-2-2-42221-1-11-112-2-1-1110000−2i32i32i3−2i3000000000000000000000000000000i3−i3−i3i300000000000000000
χ904-4-444-2-2-44-422224-2-4-2-2-212222-1-1-21-242-2-2-2-2-42221-1-11-112-2-1-11100002i3−2i3−2i32i3000000000000000000000000000000−i3i3i3−i300000000000000000
χ914-4-44-2444-42-4-4-4-4-2424-2-242222-4-4-24-224-4-422-24-2-2-222-24-4-22-2-22200000000000000000000000000000000000000000000000000000000000
χ924-4-44-24-24-42-4-422-2-224-21-222-1-122-2-212-22-422-24-2-21-1-11-221-111-1-10000000000−2i32i32i3−2i3000000000000000000000000000000i3−i3−i3i300000000000
χ934-4-44-24-24-42-4-422-2-224-21-222-1-122-2-212-22-422-24-2-21-1-11-221-111-1-100000000002i3−2i3−2i32i3000000000000000000000000000000−i3i3i3−i300000000000
χ944-4-44-24-2-442-4-422-2-224-21-222-1-122-2-21-22-24-2-22-4221-1-112-2-11-1-111004-4000000-22-220000000000000000000000000000-221-11-100000000000
χ954-4-44-24-2-442-4-422-2-224-21-222-1-122-2-21-22-24-2-22-4221-1-112-2-11-1-11100-440000002-22-200000000000000000000000000002-2-11-1100000000000
χ964-4-44-2-244-4222-4-4-242-21-2-2-1-122221-2-224-42-1-1-2-2111-1-11-22-2211-1-1000000000000000000−2i32i3−2i32i3i3i3−i3−i3i3i3−i3−i300000000000000000000000000000
χ974-4-44-2-244-4222-4-4-242-21-2-2-1-122221-2-224-42-1-1-2-2111-1-11-22-2211-1-10000000000000000002i3−2i32i3−2i3−i3−i3i3i3−i3−i3i3i300000000000000000000000000000
χ984-4-44-2-24-44222-4-4-242-21-2-2-1-122221-2-2-2-44-21122-1-11-1-112-22-2-1-1110000000000000023−2323−230000−33−33−33−3300000000000000000000000000000
χ994-4-44-2-24-44222-4-4-242-21-2-2-1-122221-2-2-2-44-21122-1-11-1-112-22-2-1-11100000000000000−2323−232300003−33−33−33−300000000000000000000000000000
χ1008888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-422-4-422-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ1018888-4-4-4-8-8-4-4-4-4-4-4-4-4-42222222222224444-2-244-2-2-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000000000000
χ10288-8-88-4-40084-44-4-84-84-4-424-44-4-224-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-48-400-4-884-4444-8-42-44-4-224-444-200000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-400-44-44-44444222-22-22-22-2-2-200006i−6i006i−6i-11-110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-400-44-44-44444222-22-22-22-2-2-20000−6i6i00−6i6i-11-1100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1068-88-88-4-400-8-44-44-8484-4-42-44-442-24-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1078-88-8-48-40048-8-4444-4-8-42-4-442-2-4444-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-4-4004-44-4444-442222-22-22-2-2-2-200006i−6i00−6i6i-1-11100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4004-44-4444-442222-22-22-2-2-2-20000−6i6i006i−6i-1-1110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-48-844444-4-44-4222-2-2-2-2-2-22224-444-2-2-4-422-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-4-8844444-4-44-4222-2-2-2-2-2-2222-44-4-42244-2-2-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.