Finite Group Databasebeta

← Group #13156617

Character table — Group #13156617

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212242424242424242424242424242424242424363636363636727272727272108108
order1222333446666666663336666666661212121212121212121236661212121212121212441212121212121212121212121212121224666666661212121212121212882424242422666688
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111
χ51111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-1-1-11111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-22-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ11222222-12222-122-1-1222-1-122-1-1-1-1-1-12-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-12022-1-1-1-1-1-1000000000000002000-1-100
χ12222222-12222-122-1-1222-1-122-1-1-1-1-1-12-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-12222-1-122-1-1-1-1-1-1-1-1-1-1-20-2-211111100000000000000-20001100
χ13222222-12222-122-1-1222-1-122-1-1-1-1-1-12-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-2-2-211-2-211111111112022-1-1-1-1-1-100000000000000-20001100
χ14222222-12222-122-1-1222-1-122-1-1-1-1-1-12-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-2-2-211-2-21111111111-20-2-2111111000000000000002000-1-100
χ15222222-1-2-222-122-1-1222-1-122-1-1-1-1-1-1211-2-2-21111-2-1-1-1-111-2-211112-222-1-1-2-211-1-1-1-111110000−i3i3−i3−i3i3i3000000000000000000−i3i300
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χ1922222-1222222-1-1222-1-1-12-1-122-12-1-1-1222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1020000000022-1-1-1-1-1-100000002-1-10000
χ2022222-1222222-1-1222-1-1-12-1-122-12-1-1-1222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-10-200000000-2-21111110000000-2110000
χ2122222-1222222-1-1222-1-1-12-1-122-12-1-1-1222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-2-211-2-211-2-211111111020000000022-1-1-1-1-1-10000000-2110000
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χ2322222-12-2-2222-1-1222-1-1-12-1-122-12-1-1-1-2-2-2111111-2-1-1-1-1-2-21111112-2-1-12211-2-2-1-1-1-11111000000000000−i3i3−i3−i3i3i300000000−i3i30000
χ2422222-12-2-2222-1-1222-1-1-12-1-122-12-1-1-1-2-2-2111111-2-1-1-1-1-2-21111112-2-1-12211-2-2-1-1-1-11111000000000000i3−i3i3i3−i3−i300000000i3−i30000
χ2522222-12-2-2222-1-1222-1-1-12-1-122-12-1-1-1-2-2-2111111-2-1-1-1-1-2-2111111-2211-2-2-1-1221111-1-1-1-1000000000000−i3i3−i3−i3i3i300000000i3−i30000
χ2622222-12-2-2222-1-1222-1-1-12-1-122-12-1-1-1-2-2-2111111-2-1-1-1-1-2-2111111-2211-2-2-1-1221111-1-1-1-1000000000000i3−i3i3i3−i3−i300000000−i3i30000
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χ282222-12222-1-122222-12-12-1-1-1-1-12-122-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002-2-1-122-1-1-1-111-2-21111-2-2111100000000
χ292222-12222-1-122222-12-12-1-1-1-1-12-122-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2211-2-21111-1-122-1-1-1-1-2-2111100000000
χ302222-12222-1-122222-12-12-1-1-1-1-12-122-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-211-2-2111111-2-2111122-1-1-1-100000000
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χ322-2-222222-2-2-22-2-2-2-222222-2-2-2-222-2-222-2-22-222-2-222-2-222-22-222-2-2000000000000000000000000000000000000-22-2-22200000000
χ332-2-22222-22-2-22-2-2-2-222222-2-2-2-222-2-22-222-22-2-222-22-2-22-22-22-2-2220000000000000000000000000000000000000000000000002-2
χ342-2-22222-22-2-22-2-2-2-222222-2-2-2-222-2-22-222-22-2-222-22-2-22-22-22-2-222000000000000000000000000000000000000000000000000-22
χ352-2-22-1222-2112-2-2-2-2-12-12-111112-1-2-2-12-212-222-2-2-1-111-1-11-11-1-11100000000000000000000−i3i300−i3i3−i3i3−i3i300−i3i3−i3i32-2-1-11100000000
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χ372-2-22-1222-2112-2-2-2-2-12-12-111112-1-2-2-12-212-222-2-2-1-111-1-11-11-1-11100000000000000000000i3−i300i3−i3i3−i3−i3i300−i3i3−i3i3-2211-1-100000000
χ382-2-22-1222-2112-2-2-2-2-12-12-111112-1-2-2-12-212-222-2-2-1-111-1-11-11-1-11100000000000000000000i3−i300i3−i3i3−i3i3−i300i3−i3i3−i32-2-1-11100000000
χ3944444-2-24444-2-2-2-2-24-2-21-2-2-2-2-21-211-2-2-24-2-2111141111-2-2-2-2111144-2-2-2-2-2-2-2-21111111100000000000000000000000000000000
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χ4144444-2-2-4-444-2-2-2-2-24-2-21-2-2-2-2-21-211-222-422-1-1-1-1-411112222-1-1-1-14-4-2-2-2-222221111-1-1-1-100000000000000000000000000000000
χ4244444-2-2-4-444-2-2-2-2-24-2-21-2-2-2-2-21-211-222-422-1-1-1-1-411112222-1-1-1-1-442222-2-2-2-2-1-1-1-1111100000000000000000000000000000000
χ434444-244-4-4-2-244444-24-24-2-2-2-2-24-244-2-4-42-4-4-4-4-4-42-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ444444-24-244-2-2-244-2-2-24-2-21-2-211-21-2-2-2-2-2-244-2-2-2-2-2111111-2-2111100000000000000000040-2-2-2-211110000000000000000000000
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χ464444-24-2-4-4-2-2-244-2-2-24-2-21-2-211-21-2-2-2222-4-4222221111-1-122-1-1-1-10000000000000000000000−2i32i3i3i3−i3−i30000000000000000000000
χ474444-24-2-4-4-2-2-244-2-2-24-2-21-2-211-21-2-2-2222-4-4222221111-1-122-1-1-1-100000000000000000000002i3−2i3−i3−i3i3i30000000000000000000000
χ484444-2-2444-2-24-2-244-2-21-2-211-2-2-2-2-2-2144-2-2-2-2-2-2-2-21111-2-21111110000000000000000000400000000-2-2-2-2111100000000000000
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χ514444-2-24-4-4-2-24-2-244-2-21-2-211-2-2-2-2-2-21-4-422222222111122-1-1-1-1-1-10000000000000000000000000000002i3−2i3−i3−i3i3i300000000000000
χ5244-4-4444004-4-44-44-4-4-44444-44-4-4-44-4-4000000000044-4-40000000000000000000000000000000000000000000000000000000000
χ5344-4-444-2004-424-4-22-4-44-2-24-4-2222-22-40000000000-2-222000000000000−2i32i30000−2i3−2i32i32i3000000000000000000000000000000000000
χ5444-4-444-2004-424-4-22-4-44-2-24-4-2222-22-40000000000-2-2220000000000002i3−2i300002i32i3−2i3−2i3000000000000000000000000000000000000
χ5544-4-44-24004-4-4-224-4-42-2-24-224-42-4-2220000000000-2-2220000000000000023−230000002323−23−2300000000000000000000000000000000
χ5644-4-44-24004-4-4-224-4-42-2-24-224-42-4-2220000000000-2-22200000000000000−2323000000−23−23232300000000000000000000000000000000
χ5744-4-44-2-2004-42-22-22-42-21-2-22-22-121-12000003i−3i3i−3i011-1-100003i−3i3i−3i0000−2i32i323−2300i3i3−i3−i3−3−33300000000000000000000000000000000
χ5844-4-44-2-2004-42-22-22-42-21-2-22-22-121-12000003i−3i3i−3i011-1-100003i−3i3i−3i00002i3−2i3−232300−i3−i3i3i333−3−300000000000000000000000000000000
χ5944-4-44-2-2004-42-22-22-42-21-2-22-22-121-1200000−3i3i−3i3i011-1-10000−3i3i−3i3i0000−2i32i3−232300i3i3−i3−i333−3−300000000000000000000000000000000
χ6044-4-44-2-2004-42-22-22-42-21-2-22-22-121-1200000−3i3i−3i3i011-1-10000−3i3i−3i3i00002i3−2i323−2300−i3−i3i3i3−3−33300000000000000000000000000000000
χ6144-4-4-24400-22-44-44-42-4-24-2-22-22-424-420000000000-2-22200000000000000000000000000000000000000000000006−66−600000000
χ6244-4-4-24400-22-44-44-42-4-24-2-22-22-424-420000000000-2-2220000000000000000000000000000000000000000000000−66−6600000000
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χ644-44-444-200-442-442-2-4-44-2-2-442-2222-2-40000000000-22-220000000000000000−2i32i30000−2i32i3−2i32i300000000000000000000000000000000
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χ714-44-44-2-200-4422-22-2-42-21-22-22-2-12-11200000−3i3i3i−3i01-11-10000−3i3i3i−3i00−23230000−2i32i33−33−3i3−i3i3−i300000000000000000000000000000000
χ724-44-4-244002-2-4-44-442-4-24-22-22-2-42-4420000000000-22-2200000000000000000000000000000000000000000000006−6−6600000000
χ734-44-4-244002-2-4-44-442-4-24-22-22-2-42-4420000000000-22-220000000000000000000000000000000000000000000000−666−600000000
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χ774-4-444-24-44-4-4422-4-44-2-2-2422-4-4-2422-2-4442-222-2-2-4-222-2-442-222-2-200000000000000000000000000000000000000000000000000
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χ804-4-444-2-2-44-4-4-222224-2-21-222221-2-1-1-22-242-2-1-111-41-1-112-22-2-1-11100000000003i−3i−3i3i3i−3i−3i3i00000000000000000000000000000000
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χ864-4-44-24-2-4422-2-4-422-24-2-2122-1-1-2122-22-2-2-4422-2-221-1-11-112-2-1-111000000000000000000000000-333-30000000000000000000000
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χ884-4-44-2-244-422422-4-4-2-21-2-2-1-122-2-22214-42-22-2-222-21-1-11-221-111-1-100000000000000000000000000002i3−2i300−i3i3−i3i300000000000000
χ894-4-44-2-24-4422422-4-4-2-21-2-2-1-122-2-2221-44-22-222-2-221-1-112-2-11-1-111000000000000000000000000000000003-3-3300000000000000
χ904-4-44-2-24-4422422-4-4-2-21-2-2-1-122-2-2221-44-22-222-2-221-1-112-2-11-1-11100000000000000000000000000000000-333-300000000000000
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χ9388-8-8-48-400-4448-8-444-8-4-42-442-24-2-444000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4800-44-8-448-8442-4-42-2-4444-44-2000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-400-444-44-44442222-22-2-2-22-2-2000006i−6i6i−6i0-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-400-444-44-44442222-22-2-2-22-2-200000−6i6i−6i6i0-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000
χ978-88-8-48-4004-44-884-44-8-4-424-4-224-24-4400000000002-22-20000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-48004-4-84-4-88442-4-4-224-4444-4-200000000002-22-20000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4004-444-44-444222-22-22-2-2-22-2000006i−6i−6i6i0-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-4004-444-44-444222-22-22-2-2-22-200000−6i6i6i−6i0-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-48-844-44444-4-4222-2-2-2-222-2-22-444-4422-2-2-4-111-12-22-2-1-11100000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-8844-44444-4-4222-2-2-2-222-2-224-4-44-4-2-2224-111-1-22-2211-1-100000000000000000000000000000000000000000000000000

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