Finite Group Databasebeta

← Group #13168245

Character table — Group #13168245

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105
size1111222222222222444444444444466668888888888888888812121212121212121212121212121212181818182424242424242424242424242424242424243636363636363636363654545454727272
order12223336666666663334666666666224436661212121212121212121212121244446666121212121212121222446612121212121212121212121212121212444466121212124444121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-111111111-1-1-1-1-1-1-1-111-11-111111-1-1-1-111111-11-1-1-111-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111-1-11111111111111111111-111111-1-1-1-11111-1-111111111-1-1111111-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-11
χ41111111111111111111111111111111-1-111111111111111111-11-1-11111-1-1-1-1-1-1-1-111-1-111-11-11-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11111-11-1
χ511111111111111111111111111111-1-111111111111111111111-111-1-1-1-11111111111-1-1-1-11-11-111-1-111111111-1-1-1111-1-1-1-1-1-1-1-1-11-1
χ611111111111111111111111111111-1-11111111111111111111-1-11-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-11-1-1-1-1-1-1111111-1-11
χ711111111111111111111111111111-1-1-1-1111111111111111111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-1-1-1-11111-1-1-1-11-11-1-1-111-1-111111-1-1
χ811111111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111
χ91111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1-111-1-111111-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-11-1
χ101111111111111111111-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1-111-1-11-1-1-1-1-111-1-111-1-1-111-11111-1-111-1-1-1-11
χ111111111111111111111-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-1-1-1111111111-1-1-111-1-1-1-111-1-1111-1-1-111-1-11111-1-11-1-1
χ121111111111111111111-111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-111-1-11-111-1-111-1-1-1-11111-11-1-1-1-1-1-1-1-111111
χ131111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-111-11-1-111-1-11111-1-111-11-1-1-1-1-1-111-1-1111
χ141111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1111111-1-11111-1-1-1111-1-11111-1-111-1-11-1-1-111-1-111-1-1111-1-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-111111-1-111-1-111-111-11111-1-1-1-111-1-11
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1111111111-1-1-1-111-1-111-1-1111111-1-1-11-1
χ17222222-122-1-1222-12-1-122-1-12-12-12-1-10022-1-1-1-1-12222-1-1-1-1-1-1-1-12022000022-1-1-1-122220000-10202-100-1-1-1-1-1-1-1-10002-1-1000000000-10
χ18222222-122-1-1222-12-1-122-1-12-12-12-1-10022-1-1-1-1-12222-1-1-1-1-1-1-1-1-202-2000022-1-111-2-2-2-2000010-202-1001111-1-1-1-1000-21100000000010
χ19222222-122-1-1222-12-1-122-1-12-12-12-1-100-2-2-1-1-1-1-12222-1-1-1-1-1-1-1-120-220000-2-211-1-122-2-20000-1020-2100-1-1-1-11111000-21100000000010
χ20222222-122-1-1222-12-1-122-1-12-12-12-1-100-2-2-1-1-1-1-12222-1-1-1-1-1-1-1-1-20-2-20000-2-21111-2-222000010-20-2100111111110002-1-1000000000-10
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χ22222222-122-1-1222-12-1-12-2-1-12-12-12-1-10022-1-1-1-11-2-2-2-211111111-20-22000022-1-1-1-1-2-22200001020-2100-1-111-1-111000-2-1-100000000010
χ23222222-122-1-1222-12-1-12-2-1-12-12-12-1-100-2-2-1-1-1-11-2-2-2-211111111202-20000-2-2111122220000-10-202-10011-1-111-1-1000-2-1-100000000010
χ24222222-122-1-1222-12-1-12-2-1-12-12-12-1-100-2-2-1-1-1-11-2-2-2-211111111-20220000-2-211-1-1-2-2-2-2000010202-100-1-11111-1-1000211000000000-10
χ2522222-122-1222-1-1222-1-122-1-1-1-12-12-12222-1-1-1-12-12-1-1-1-122-1-1-1-1022022-1-1-1-12200000000-1-1020-1-12-1-10000-1-1-1-1202000-1-1000000-100
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χ2722222-122-1222-1-1222-1-122-1-1-1-12-12-1-2-222-1-1-1-12-12-1-1-1-122-1-1-1-10-220-2-211-1-12200000000110-201-12110000-1-1-1-1-20-200011000000100
χ2822222-122-1222-1-1222-1-122-1-1-1-12-12-1-2-2-2-2-1-1-1-12-12-1-1-1-122-1-1-1-10-2-20-2-21111-2-200000000110-2011-21100001111202000-1-1000000-100
χ2922222-122-1222-1-1222-1-1-22-1-1-1-12-12-12222-1-1-1-1-21-21111-2-211110-2-2022-1-1-1-12200000000-1-10-2011-2110000-1-111-202000-1-1000000100
χ3022222-122-1222-1-1222-1-1-22-1-1-1-12-12-122-2-2-1-1-1-1-21-21111-2-211110-22022-1-111-2-200000000-1-10-201-1211000011-1-120-200011000000-100
χ3122222-122-1222-1-1222-1-1-22-1-1-1-12-12-1-2-222-1-1-1-1-21-21111-2-2111102-20-2-211-1-1220000000011020-11-2-1-10000-1-11120-200011000000-100
χ3222222-122-1222-1-1222-1-1-22-1-1-1-12-12-1-2-2-2-2-1-1-1-1-21-21111-2-211110220-2-21111-2-20000000011020-1-12-1-1000011-1-1-202000-1-1000000100
χ332222-122-1222-1222-1-12-12-12-12-1-1-1-122200-1-1-1-122-1-1-122-1-1-1-1-1-12202-1-122000022-1-10022-1-12-1-1200-1-1-1-1-1-1000002000000-1-1000000-1
χ342222-122-1222-1222-1-12-12-12-12-1-1-1-122200-1-1-1-122-1-1-122-1-1-1-1-1-1-220-2-1-1220000-2-21100-2-2-1-1-2-11200-1-1111100000-2000000110000001
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χ362222-122-1222-1222-1-12-12-12-12-1-1-1-12-2-200-1-1-1-122-1-1-122-1-1-1-1-1-1-2-20-211-2-20000-2-211002211-211-200111111000002000000-1-1000000-1
χ372222-122-1222-1222-1-12-1-2-12-12-1-1-1-122200-1-1-1-1-2-2111-2-21111112-20-2-1-1220000-2-2-1-10022-1-1211-2001111-1-100000-2000000-1-10000001
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χ392222-122-1222-1222-1-12-1-2-12-12-1-1-1-12-2-200-1-1-1-1-2-2111-2-2111111220-211-2-20000-2-2-1-100-2-2112-11200-1-111-1-100000200000011000000-1
χ402222-122-1222-1222-1-12-1-2-12-12-1-1-1-12-2-200-1-1-1-1-2-2111-2-2111111-220211-2-200002211002211-2-1-1200-1-1-1-11100000-2000000-1-10000001
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χ1048-8-88-4-4-44444-44-4-442220-2-2-2-2-222-220000-11-1100000006i−6i−3i3i3i−3i0000000000000000000000000000000000000000000000000000000
χ1058-8-88-4-4-44444-44-4-442220-2-2-2-2-222-220000-11-110000000−6i6i3i−3i−3i3i0000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).