Finite Group Databasebeta

← Group #13155819

Character table — Group #13155819

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212121212121212121212121212181818181818242424242424242424242424363636727272727272108108
order12223334466666666633366666666612121212121212121212366612121212121212122244666688121212122424242424242424242424242424242444121212126666661212121212122662466121288
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
χ3111111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-11111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-111-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-11111
χ51111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11-1-111-1-1
χ61111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-111-1-111
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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χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000-2-2-2-2-2-200000000000022200000000
χ11222222-122222-1-1-12222-1-122-1-1-1-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1220022222200002222-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-100000000020-1-10000
χ12222222-122222-1-1-12222-1-122-1-1-1-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-122002222-2-20000-2-2-2-2111111111111000000-1-1-1-1-1-1000000000-20110000
χ13222222-122222-1-1-12222-1-122-1-1-1-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2-2-2-22200002222-1-1-1-1-1-1-1-1-1-1-1-1000000111111000000000-20110000
χ14222222-122222-1-1-12222-1-122-1-1-1-1-1-12-1222-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200-2-2-2-2-2-20000-2-2-2-211111111111100000011111100000000020-1-10000
χ1522222-12222-1-12222-12-12-1-1-122-1-12-1-122-1-1222222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-100-1-1-1-1000000000000000022-1-1-1-122-1-1-1-122-1-1-1-12-1-100000000
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χ1922222-12-2-22-1-12222-12-12-1-1-122-1-12-1-1-2-211-2-2-2-2-2-2-1-1-1-1111111110000−i3−i3i3i300−i3−i3i3i3000000000000000022-1-1-1-100−i3−i3i3i300−i3−i3i3i3-21100000000
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χ262222-12222-122222-12-1-1-12-1-1-1-122-12-12-122-1-12-1-1-1-1-1-1-122-1-1-1-1-1-100-2-20000-2-2-2-2-2-21111-2-2-2-2111111110000000000001111110000200-1-100
χ2722-2-22220022-22-2-2-2-2-22222-22-22-2-2-2-2000000000022-2-200000000000000002−2000022−2−222−2−22222−2−2−2−22i−2i2i2i−2i−2i000000000000000000000−i2i2
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χ422-22-22-122-2-211-2-222-1-2-12-111-2-2112-1-1-2-2-11-2-22222-111-1-11-11-1-111-22001-11-100i3−i3−i3i3000000000000000000−i3i3−i3i3-221-11-100i3−i3−i3i30−i3i300000000
χ432-22-22-12-22-211-2-222-1-2-12-111-2-2112-1-1221-122-2-2-2-2-111-11-11-111-1-1002-2−i3i3i3−i300-11-11000000000000000000−i3i3−i3i300−i3i3i3−i32-2-11-110i3−i300000000
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χ774-44-44-2-24-4-42222-24-2-4-2-212222-1-1-21-22-4-2222-24-2-21-1-111-1-2211-1-1-44002-22-200000000000000000000000000002-2-11-1100000000000000000
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χ824-44-4-24-24-42-4-422-2-242-21-222-1-1221-2-2224-4-1-1-2-2111-1-11-22-2211-1-10000000000000000002i3−2i32i3−2i3−i3−i3i3i3−i3−i3i3i300000000000000000000000000000
χ834-44-4-24-2-442-4-422-2-242-21-222-1-1221-2-2-2-2-441122-1-11-1-112-22-2-1-1110000000000000023−2323−230000−33−33−33−3300000000000000000000000000000
χ844-44-4-24-2-442-4-422-2-242-21-222-1-1221-2-2-2-2-441122-1-11-1-112-22-2-1-11100000000000000−2323−232300003−33−33−33−300000000000000000000000000000
χ854-44-4-2-244-4222-4-44-2-221-2-2-1-12222-2-21-42-22224-2-2-21-1-11-221-111-1-10000000000−2i32i32i3−2i3000000000000000000000000000000i3−i3−i3i300000000000
χ864-44-4-2-244-4222-4-44-2-221-2-2-1-12222-2-21-42-22224-2-2-21-1-11-221-111-1-100000000002i3−2i3−2i32i3000000000000000000000000000000−i3i3i3−i300000000000
χ874-44-4-2-24-44222-4-44-2-221-2-2-1-12222-2-214-22-2-2-2-42221-1-112-2-11-1-111004-4000000-22-220000000000000000000000000000-221-11-100000000000
χ884-44-4-2-24-44222-4-44-2-221-2-2-1-12222-2-214-22-2-2-2-42221-1-112-2-11-1-11100-440000002-22-200000000000000000000000000002-2-11-1100000000000
χ894-4-4444400-4-44-44-4-4-44444-44-44-44-4-4-400000000004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ904-4-4444-200-4-442-22-4-444-2-2-442-22-222-40000000000-22-2200000000000000000000000000i6−i6−i6i6i6i6−i6−i6−i6−i6i6i600000000000000000000000000000
χ914-4-4444-200-4-442-22-4-444-2-2-442-22-222-40000000000-22-2200000000000000000000000000−i6i6i6−i6−i6−i6i6i6i6i6−i6−i600000000000000000000000000000
χ924-4-444-2400-42-2-44-4-424-24-22-2-442-2-4220000000000-22-22000000000000000000000000000000000000000023−23−232300000000000000000000000
χ934-4-444-2400-42-2-44-4-424-24-22-2-442-2-4220000000000-22-220000000000000000000000000000000000000000−232323−2300000000000000000000000
χ944-4-44-244002-44-44-42-4-2-2-242-22-2-442-420000000000-22-2200000000000000000000006−6−6600006−66−6−66−6600000000000000000000000000000
χ954-4-44-244002-44-44-42-4-2-2-242-22-2-442-420000000000-22-220000000000000000000000−666−60000−66−666−66−600000000000000000000000000000
χ964-4-44-24-2002-442-222-4-2-21-22-2-112-2-12200003i−3i00−3i3i1-11-10000−3i3i3i−3i000000000000006−6−66i6−i6−i6i6−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ1300000000000000000000000000000
χ974-4-44-24-2002-442-222-4-2-21-22-2-112-2-12200003i−3i00−3i3i1-11-10000−3i3i3i−3i00000000000000−666−6−i6i6i6−i6ζ5−ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ1300000000000000000000000000000
χ984-4-44-24-2002-442-222-4-2-21-22-2-112-2-1220000−3i3i003i−3i1-11-100003i−3i−3i3i000000000000006−6−66−i6i6i6−i6ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ2300000000000000000000000000000
χ994-4-44-24-2002-442-222-4-2-21-22-2-112-2-1220000−3i3i003i−3i1-11-100003i−3i−3i3i00000000000000−666−6i6−i6−i6i6−ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ2300000000000000000000000000000
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
χ10288-8-88-4-4008-44-444-84-8-4-42-44-442-24-24000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ10388-8-8-4-4800-4-448-8-84442-4-42-2-44-4444-2000000000022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ10488-8-8-4-4-400-4-44-4444442222-22-22-2-2-2-200006i−6i006i−6i-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-4-400-4-44-4444442222-22-22-2-2-2-20000−6i6i00−6i6i-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-48-844444-4-4-44222-2-2-2-2-2-222244-44-2-2-4-422-111-12-22-2-1-11100000000000000000000000000000000000000000000000000000000000
χ1078-88-8-4-4-4-8844444-4-4-44222-2-2-2-2-2-2222-4-44-42244-2-2-111-1-22-2211-1-100000000000000000000000000000000000000000000000000000000000
χ1088-8-888-4-400-84-44-44-848-4-424-44-4-224-2400000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-480044-4-88-844-42-4-4-224-44-444-200000000002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-40044-44-4444-4222-22-22-22-2-2-200006i−6i00−6i6i-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-40044-44-4444-4222-22-22-22-2-2-20000−6i6i006i−6i-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000000

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