Finite Group Databasebeta

← Group #13161985

Character table — Group #13161985

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size112222222222244444444444444444444444444448888888888888888888888888888888888888363636363636363636363636727272727272727272727272
order1223334466666333336666666666666666612121212121226666666666666666666666666612121212121212121212224444441212121266881212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-11-11-11-1-1-111-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-11-11-1-1-1-1-1-1-1-1-11-11-11-1-1-1-111
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1
χ511111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-11-1-1-11111111-1-111-1-1-1-1-111
χ711111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-11-11-1-1111111-111-1-11-1-111-1-1
χ811111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111
χ9222222-2-2222222222222222222222222222-2-2-2-2-2-2000000000000000000000000000-2-2-2-2-2-2-2-2-2-200002-20000000000002-20000
χ10222222-2-2222222222222222222222222222-2-2-2-2-2-2000000000000000000000000000-2-2-2-2-2-2-2-2-2-20000-22000000000000-220000
χ1122222-122222-122-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-1222-122222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10202000000000-1020-10000-1-1
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χ1322222-122222-122-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-1222-1-2-2-2-2-211-2-2-2-2111111111111111122-1-1-1-1-1-1-1-10202000000000-10-20-1000011
χ1422222-122222-122-1-1-1-12-122-1-1-1-1-1-1-1-12-1-1-1-12-1222-1-2-2-2-2-211-2-2-2-2111111111111111122-1-1-1-1-1-1-1-10-20-2000000000102010000-1-1
χ152222-122222-122-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-1222-12222-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1202000000000-1020-1000-1-100
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χ182222-122222-122-12-1-1-1-12-1-122-1-1-1-1-1-1-12-1-1-1-1222-12-2-2-211-2-21111-2-2-2-2111111111111-1-122-1-1-1-1-1-1-20-200000000010201000-1-100
χ19222-12222-1-122-1-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-1222-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-100002222-1-1-1-1000000-1-10000
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χ22222-12222-1-122-1-1-12-1-122-1-1-1-122-1-1-1-1-1-12-1-122-1-122-211-2-2-2-211111111-2-2-2-211111111-1-1-1-122-1-1-1-10000-2-222-1-1-1-1000000110000
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χ2722-22222-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-22-2-220000000000000000000000000002-22-22-222-2-2020-20000000002000-2000000
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χ2922-2222-22-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222222-22-222-2000000000000000000000000000-22-22-22-2-22220-20000000002000-20000000
χ3022-2222-22-2-222222222-2-2-2-2-2-2-2-2-2-2-2-222222-22-222-2000000000000000000000000000-22-22-22-2-222-202000000000-200020000000
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χ414444-2-24444-2-24-2-2111-2-2-2-2-2-2111111-2-2111-2-244-2-2444-2-2-2-2-2-2-2-2-2-2-2-2111111111111-2-2-2-2111111000000000000000000000000
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χ53444-2-2-244-2-2-2-2-2111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2-2-24-2-2-2-2-2-2111111111111−1−3i32−1+3i32−1+3i32−1−3i32−1+3i32−1−3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000
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χ57444-2-2-2-4-4-2-2-2-2-2111−1−3i32−1+3i32-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32111−1−3i32−1+3i322222220−2i32i30000i3i3−i3−i3i3i3−i3−i33-3-33−3−i323−i323−i32−3−i32−3+i323+i323+i32−3+i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000
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χ59444-2-2-2-4-4-2-2-2-2-2111−1+3i32−1−3i32-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32111−1+3i32−1−3i322222220−2i32i30000i3i3−i3−i3i3i3−i3−i3-333-33−i32−3−i32−3−i323−i323+i32−3+i32−3+i323+i32-1-1-1-1-1-11−3i321+3i321−3i321+3i32000000000000000000000000
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χ854-404440000-4-4-444444000000000000-4-4-4-4-400000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i000000000000
χ864-404440000-4-4-444444000000000000-4-4-4-4-40000000000000000000000000000000000000000000000000−2i2i−2i2i−2i2i000000000000
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χ884-40-24400−2i32i3-4-42-2-24-2-200−2i32i3−2i32i300−2i32i3−2i32i322-4220000000000000000000000000000000000000000000000000−2i2i−2ζ72ζ7−2ζ112ζ11000000000000
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χ928-808-4800004-8-8-48-4-4-40000000000004-84440000000000000000000000000000000000000000000000000000000000000000000
χ938-808-4-4000044-8-4-42220000006-66-6-6644-2-2-20000000000000000000000000000000000000000000000000000000000000000000
χ948-808-4-4000044-8-4-4222000000-66-666-644-2-2-20000000000000000000000000000000000000000000000000000000000000000000
χ958-80-48-400−4i34i3-844-42-42200−4i34i32i3−2i3002i3−2i32i3−2i34-24-2-20000000000000000000000000000000000000000000000000000000000000000000
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χ978-80-4-4800−4i34i34-842-4-422002i3−2i3−4i34i3002i3−2i32i3−2i3-244-2-20000000000000000000000000000000000000000000000000000000000000000000
χ988-80-4-48004i3−4i34-842-4-42200−2i32i34i3−4i300−2i32i3−2i32i3-244-2-20000000000000000000000000000000000000000000000000000000000000000000
χ998-80-4-4-400−4i34i3444222−1−3i3−1+3i3002i3−2i32i3−2i36-6−3−i33+i33−i3−3+i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000
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χ1018-80-4-4-4004i3−4i3444222−1−3i3−1+3i300−2i32i3−2i32i3-663+i3−3−i3−3+i33−i3-2-2-21+3i31−3i30000000000000000000000000000000000000000000000000000000000000000000
χ1028-80-4-4-4004i3−4i3444222−1+3i3−1−3i300−2i32i3−2i32i36-6−3+i33−i33+i3−3−i3-2-2-21−3i31+3i30000000000000000000000000000000000000000000000000000000000000000000

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