Finite Group Databasebeta

← Group #11786739

Character table — Group #11786739

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size11112222222222222222224444444444444444444444888888888888888888881212121212121212121212122424242424242424242424242424242424243636363636363636
order1222223344446666661212121234444666666612121212121212121212661212121212121212121212121212121212124444121212121212121244888812121212242424242424242422444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ611111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111
χ91-11-1-11111-11-111-1-1-1-111-1-11i−ii−i1-1-11-1-1111-1-1-111-1-111-1iii−i−i−ii−i1-1iiii−i−i−i−i11-1-11111-1-1-1-1i−ii−i1-1ii−i−iii−i−i11-1-11-11-1ii−i−i
χ101-11-1-11111-11-111-1-1-1-111-1-11i−ii−i1-1-11-1-1111-1-1-111-1-111-1iii−i−i−ii−i1-1iiii−i−i−i−i11-1-11111-1-1-1-1−iii−i-11−i−iiiii−i−i-1-111-11-11−i−iii
χ111-11-1-11111-11-111-1-1-1-111-1-11i−ii−i1-1-11-1-1111-1-1-111-1-111-1iii−i−i−ii−i1-1iiii−i−i−i−i-1-111-1-1-1-11111i−i−ii1-1ii−i−i−i−iii11-1-1-11-11−i−iii
χ121-11-1-11111-11-111-1-1-1-111-1-11i−ii−i1-1-11-1-1111-1-1-111-1-111-1iii−i−i−ii−i1-1iiii−i−i−i−i-1-111-1-1-1-11111−ii−ii-11−i−iii−i−iii-1-1111-11-1ii−i−i
χ131-11-1-11111-11-111-1-1-1-111-1-11−ii−ii1-1-11-1-1111-1-1-111-1-111-1−i−i−iiii−ii1-1−i−i−i−iiiii11-1-11111-1-1-1-1i−i−ii-11ii−i−i−i−iii-1-111-11-11ii−i−i
χ141-11-1-11111-11-111-1-1-1-111-1-11−ii−ii1-1-11-1-1111-1-1-111-1-111-1−i−i−iiii−ii1-1−i−i−i−iiiii11-1-11111-1-1-1-1−ii−ii1-1−i−iii−i−iii11-1-11-11-1−i−iii
χ151-11-1-11111-11-111-1-1-1-111-1-11−ii−ii1-1-11-1-1111-1-1-111-1-111-1−i−i−iiii−ii1-1−i−i−i−iiiii-1-111-1-1-1-11111i−ii−i-11ii−i−iii−i−i-1-1111-11-1−i−iii
χ161-11-1-11111-11-111-1-1-1-111-1-11−ii−ii1-1-11-1-1111-1-1-111-1-111-1−i−i−iiii−ii1-1−i−i−i−iiiii-1-111-1-1-1-11111−iii−i1-1−i−iiiii−i−i11-1-1-11-11ii−i−i
χ1722222222-2-2-2-2222222-2-2-2-2200002222222-2-2-2-2-2-2-2-2-2-22200000000-2-20000000000000000000000000000000000000000002-22-2
χ1822222222-2-2-2-2222222-2-2-2-2200002222222-2-2-2-2-2-2-2-2-2-22200000000-2-2000000000000000000000000000000000000000000-22-22
χ192222222-122222-122-1-12222-12222-12-1-1-1-122-12-1-1-1-1-1-1-1-1-122-122-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000220022-1-1-1-10000-1-1-1-100000000
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χ272222-2-2222-2-22222222222220000-2-2-2222-2-22-22-22222-2-2-200000000-2-20000000000000000000000000000000000000022-2-20000
χ282222-2-2222-2-22222222222220000-2-2-2222-2-22-22-22222-2-2-200000000-2-200000000000000000000000000000000000000-2-2220000
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χ322222-2-22-1-222-22-122-1-1-2-2-2-2-122-2-21-21-1-1-1-22121-11111-1112-212-21-1-1-1-1-1-111-1-111000000000000000000i3−i3i3−i30000i3−i3i3−i300000000
χ332222-2-22-1-222-22-122-1-1-2-2-2-2-1-2-2221-21-1-1-1-22121-11111-111-22-1-22-111-1-111-1-111-1-1000000000000000000−i3i3−i3i30000i3−i3i3−i300000000
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χ362222-2-2-12-222-2-12-1-1221111-122-2-2-21-2-1-1-11-1-2-1-221111211-11-2-11-222-1-1-1-111-1-1110000−3−333−3−3330000000000−33−33000000000000
χ372222-2-2-12-222-2-12-1-1221111-1-2-222-21-2-1-1-11-1-2-1-2211112111-121-12-2-2-1-111-1-111-1-1000033−3−333−3−30000000000−33−33000000000000
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χ422-22-22-222-2-22222-2-2-2-2-2-2222−2i2i2i−2i-2222-2-2-22-2-22-2-2-2222-22−2i2i2i2i−2i−2i−2i2i2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000
χ432-22-22-22-1-2-2222-1-2-211-2-222-12i−2i−2i2i12-1-111-221-2-1111-1-1-11-12i−2ii−2i2i−i−ii-11−i−iiiii−i−i0000000000000000003−3−330000−i3i3i3−i300000000
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χ452-22-22-22-1-2-2222-1-2-211-2-222-1−2i2i2i−2i12-1-111-221-2-1111-1-1-11-1−2i2i−i2i−2iii−i-11ii−i−i−i−iii0000000000000000003−3−330000i3−i3−i3i300000000
χ462-22-22-22-1-2-2222-1-2-211-2-222-1−2i2i2i−2i12-1-111-221-2-1111-1-1-11-1−2i2i−i2i−2iii−i-11ii−i−i−i−iii000000000000000000−333−30000−i3i3i3−i300000000
χ472-22-22-2-12-2-222-1211-2-211-1-1-12i−2i−2i2i-2-12-1111-1-212-211-1-121-1−ii−2ii−i2i2i−2i-11−i−iiiii−i−i000033−3−3−3−3330000000000i3−i3−i3i3000000000000
χ482-22-22-2-12-2-222-1211-2-211-1-1-12i−2i−2i2i-2-12-1111-1-212-211-1-121-1−ii−2ii−i2i2i−2i-11−i−iiiii−i−i0000−3−33333−3−30000000000−i3i3i3−i3000000000000
χ492-22-22-2-12-2-222-1211-2-211-1-1-1−2i2i2i−2i-2-12-1111-1-212-211-1-121-1i−i2i−ii−2i−2i2i-11ii−i−i−i−iii000033−3−3−3−3330000000000−i3i3i3−i3000000000000
χ502-22-22-2-12-2-222-1211-2-211-1-1-1−2i2i2i−2i-2-12-1111-1-212-211-1-121-1i−i2i−ii−2i−2i2i-11ii−i−i−i−iii0000−3−33333−3−30000000000i3−i3−i3i3000000000000
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χ532-22-2-222-12-22-22-1-2-21122-2-2-12i−2i2i−2i-1-21-11122-1-211-1-111-1-112i2i−i−2i−2ii−ii-11−i−i−i−iiiii0000000000002i−2i002-2−i−iii0000-1-11100000000
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χ552-22-2-222-12-22-22-1-2-21122-2-2-1−2i2i−2i2i-1-21-11122-1-211-1-111-1-11−2i−2ii2i2i−ii−i-11iiii−i−i−i−i0000000000002i−2i00-22−i−iii000011-1-100000000
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χ874-44-4-44-2-24-44-4-2-22222-2-22214i−4i4i−4i-2221-1-1-2-2-222211-1-1-21-1−2i−2i−2i2i2i2i−2i2i1-1iiii−i−i−i−i00000000000000000000000000000000000000
χ884-44-4-44-2-24-44-4-2-22222-2-2221−4i4i−4i4i-2221-1-1-2-2-222211-1-1-21-12i2i2i−2i−2i−2i2i−2i1-1−i−i−i−iiiii00000000000000000000000000000000000000
χ894-44-4-44-2-2-44-44-2-2222222-2-210000-2221-1-1-222-2-2-2-1-11121-100000000-113i−3i3i−3i−3i3i−3i3i00000000000000000000000000000000000000
χ904-44-4-44-2-2-44-44-2-2222222-2-210000-2221-1-1-222-2-2-2-1-11121-100000000-11−3i3i−3i3i3i−3i3i−3i00000000000000000000000000000000000000
χ914-4-4400440000-4-4-444-4000040000000-4-4400000000000000000000000000000002i−2i−2i2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000
χ924-4-4400440000-4-4-444-4000040000000-4-440000000000000000000000000000000−2i2i2i−2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000
χ934-4-4400-2400002-42-24-423−23−2323-2000000022-200000023−23−23230000000000000000000002i−2i−2i2i−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ1100000000000000000000000000
χ944-4-4400-2400002-42-24-423−23−2323-2000000022-200000023−23−2323000000000000000000000−2i2i2i−2iζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ1100000000000000000000000000
χ954-4-4400-2400002-42-24-4−232323−23-2000000022-2000000−232323−230000000000000000000002i−2i−2i2iζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ1100000000000000000000000000
χ964-4-4400-2400002-42-24-4−232323−23-2000000022-2000000−232323−23000000000000000000000−2i2i2i−2i−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ1100000000000000000000000000
χ9788-8-8008-40000-848-84-40000-400000004-44000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-800-4-4000044-444-443−4343−4320000000-22-2000000−2323−232300000000000000000000000000000000000000000000000000000000000
χ9988-8-800-4-4000044-444-4−4343−434320000000-22-200000023−2323−2300000000000000000000000000000000000000000000000000000000000
χ1008-8-88008-40000-84-88-440000-4000000044-4000000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-8800-4-40000444-4-4443−43−434320000000-2-22000000−232323−2300000000000000000000000000000000000000000000000000000000000
χ1028-8-8800-4-40000444-4-44−434343−4320000000-2-2200000023−23−232300000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.