Finite Group Databasebeta

← Group #13156542

Character table — Group #13156542

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212242424242424242424242424242424242424363636363636727272727272108108
order12223334466666666633366666666612121212121212121212366612121212121212124412121212121212121212121212121212246666666612121212121212128824242424441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11-1-111-1-1
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
χ61111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11-111-1-111
χ81111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
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
χ11222222-1222222-1-12-122-1-12-1-12-1-1-1-12222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-12022-1-1-1-1-1-10000000000000020-1-10000
χ12222222-1222222-1-12-122-1-12-1-12-1-1-1-12222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-12222-1-1-1-122-1-1-1-1-1-1-1-1-20-2-211111100000000000000-20110000
χ13222222-1222222-1-12-122-1-12-1-12-1-1-1-12222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-2-2-2-21111-2-2111111112022-1-1-1-1-1-100000000000000-20110000
χ14222222-1222222-1-12-122-1-12-1-12-1-1-1-12222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-2-2-2-21111-2-211111111-20-2-21111110000000000000020-1-10000
χ15222222-1-2-22222-1-12-122-1-12-1-12-1-1-1-12-2-2-2111111-2-1-1-1-1-2-21111112-222-1-111-2-2-1-1-1-111110000−i3i3−i3−i3i3i30000000000000000−i3i30000
χ16222222-1-2-22222-1-12-122-1-12-1-12-1-1-1-12-2-2-2111111-2-1-1-1-1-2-21111112-222-1-111-2-2-1-1-1-111110000i3−i3i3i3−i3−i30000000000000000i3−i30000
χ17222222-1-2-22222-1-12-122-1-12-1-12-1-1-1-12-2-2-2111111-2-1-1-1-1-2-2111111-22-2-211-1-1221111-1-1-1-10000−i3i3−i3−i3i3i30000000000000000i3−i30000
χ18222222-1-2-22222-1-12-122-1-12-1-12-1-1-1-12-2-2-2111111-2-1-1-1-1-2-2111111-22-2-211-1-1221111-1-1-1-10000i3−i3i3i3−i3−i30000000000000000−i3i30000
χ1922222-1222-12-1222-122-12-1-1-1-1-12-122-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022-1-122-1-1-1-1-1-122-1-1-1-122-1-1-1-100000000
χ2022222-1222-12-1222-122-12-1-1-1-1-12-122-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002-2-1-122-1-1-1-111-2-21111-2-2111100000000
χ2122222-1222-12-1222-122-12-1-1-1-1-12-122-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2211-2-21111-1-122-1-1-1-1-2-2111100000000
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χ232222-122222-12-12222-1-1-12-122-1-12-1-1-1-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-1020000000022-1-1-1-1-1-10000000200-1-100
χ242222-122222-12-12222-1-1-12-122-1-12-1-1-1-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-122-1-12222-1-1-1-1-1-1-1-1-1-10-200000000-2-21111110000000-2001100
χ252222-122222-12-12222-1-1-12-122-1-12-1-1-1-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-2-2-21111111111020000000022-1-1-1-1-1-10000000-2001100
χ262222-122222-12-12222-1-1-12-122-1-12-1-1-1-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-211-2-2-2-211111111110-200000000-2-21111110000000200-1-100
χ272222-122-2-22-12-12222-1-1-12-122-1-12-1-1-111-2-2-21111-2-1-1-1-111-2-211112-2-1-122-2-211-1-1-1-11111000000000000−i3i3−i3−i3i3i30000000000−i3i300
χ282222-122-2-22-12-12222-1-1-12-122-1-12-1-1-111-2-2-21111-2-1-1-1-111-2-211112-2-1-122-2-211-1-1-1-11111000000000000i3−i3i3i3−i3−i30000000000i3−i300
χ292222-122-2-22-12-12222-1-1-12-122-1-12-1-1-111-2-2-21111-2-1-1-1-111-2-21111-2211-2-222-1-11111-1-1-1-1000000000000−i3i3−i3−i3i3i30000000000i3−i300
χ302222-122-2-22-12-12222-1-1-12-122-1-12-1-1-111-2-2-21111-2-1-1-1-111-2-21111-2211-2-222-1-11111-1-1-1-1000000000000i3−i3i3i3−i3−i30000000000−i3i300
χ312-22-22222-2-222-2-2-2-22-2222-2-2-2222-2-2-22-2-22-222-2-222-2-222-22-222-2-20000000000000000000000000000000000000000000000002i−2i
χ322-22-22222-2-222-2-2-2-22-2222-2-2-2222-2-2-22-2-22-222-2-222-2-222-22-222-2-2000000000000000000000000000000000000000000000000−2i2i
χ332-22-2222-22-222-2-2-2-22-2222-2-2-2222-2-2-2-222-22-2-222-22-2-22-22-22-2-2220000000000000000000000000000000000002i−2i2i2i−2i−2i00000000
χ342-22-2222-22-222-2-2-2-22-2222-2-2-2222-2-2-2-222-22-2-222-22-2-22-22-22-2-222000000000000000000000000000000000000−2i2i−2i−2i2i2i00000000
χ352-22-22-12-2212-1-2-2-212-2-12-1111-12-1-2-21-22-1-22-2-2221-111-11-11-111-1-100000000000000000000−i3i300−i3i3−i3i33−3003−33−32i−2i−i−iii00000000
χ362-22-22-12-2212-1-2-2-212-2-12-1111-12-1-2-21-22-1-22-2-2221-111-11-11-111-1-100000000000000000000−i3i300−i3i3−i3i3−3300−33−33−2i2iii−i−i00000000
χ372-22-22-12-2212-1-2-2-212-2-12-1111-12-1-2-21-22-1-22-2-2221-111-11-11-111-1-100000000000000000000i3−i300i3−i3i3−i33−3003−33−3−2i2iii−i−i00000000
χ382-22-22-12-2212-1-2-2-212-2-12-1111-12-1-2-21-22-1-22-2-2221-111-11-11-111-1-100000000000000000000i3−i300i3−i3i3−i3−3300−33−332i−2i−i−iii00000000
χ3944444-24-4-4-24-2444-244-24-2-2-2-2-24-244-2-4-42-4-4-4-4-4-42-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ4044444-2-244-24-24-2-2-2-24-2-21-211-2-21-2-2-244-2-2-2-2-2-2-2-21111-2-211111100000000000000000040-2-2-2-211110000000000000000000000
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χ4244444-2-2-4-4-24-24-2-2-2-24-2-21-211-2-21-2-2-2-4-422222222111122-1-1-1-1-1-10000000000000000000000−2i32i3i3i3−i3−i30000000000000000000000
χ4344444-2-2-4-4-24-24-2-2-2-24-2-21-211-2-21-2-2-2-4-422222222111122-1-1-1-1-1-100000000000000000000002i3−2i3−i3−i3i3i30000000000000000000000
χ444444-24-2444-24-2-2-24-2-2-21-2-2-2-2-21-211-2-2-24-2-2111141111-2-2-2-2111144-2-2-2-2-2-2-2-21111111100000000000000000000000000000000
χ454444-24-2444-24-2-2-24-2-2-21-2-2-2-2-21-211-2-2-24-2-2111141111-2-2-2-21111-4-422222222-1-1-1-1-1-1-1-100000000000000000000000000000000
χ464444-24-2-4-44-24-2-2-24-2-2-21-2-2-2-2-21-211-222-422-1-1-1-1-411112222-1-1-1-14-4-2-2-2-222221111-1-1-1-100000000000000000000000000000000
χ474444-24-2-4-44-24-2-2-24-2-2-21-2-2-2-2-21-211-222-422-1-1-1-1-411112222-1-1-1-1-442222-2-2-2-2-1-1-1-1111100000000000000000000000000000000
χ484444-2-2444-2-2-2-244-24-21-2-21-2-21-2-2-2-21-2-2-244-2-2-2-2-2111111-2-211110000000000000000000400000000-2-2-2-2111100000000000000
χ494444-2-2444-2-2-2-244-24-21-2-21-2-21-2-2-2-21-2-2-244-2-2-2-2-2111111-2-211110000000000000000000-4000000002222-1-1-1-100000000000000
χ504444-2-24-4-4-2-2-2-244-24-21-2-21-2-21-2-2-2-21222-4-4222221111-1-122-1-1-1-1000000000000000000000000000000−2i32i3i3i3−i3−i300000000000000
χ514444-2-24-4-4-2-2-2-244-24-21-2-21-2-21-2-2-2-21222-4-4222221111-1-122-1-1-1-10000000000000000000000000000002i3−2i3−i3−i3i3i300000000000000
χ5244-4-4444004-4-444-4-4-4-444444-4-4-4-44-4-4000000000044-4-40000000000000000000000000000000000000000000000000000000000
χ5344-4-444-2004-4-44-22-42-44-2-24-22-422-22-40000000000-2-2220000000000000023−230000002323−23−2300000000000000000000000000000000
χ5444-4-444-2004-4-44-22-42-44-2-24-22-422-22-40000000000-2-22200000000000000−2323000000−23−23232300000000000000000000000000000000
χ5544-4-44-2400-2-4244-42-4-4-24-2-2-222-424-420000000000-2-22200000000000000000000000000000000000000000000006−66−600000000
χ5644-4-44-2400-2-4244-42-4-4-24-2-2-222-424-420000000000-2-2220000000000000000000000000000000000000000000000−66−6600000000
χ5744-4-4-2440042-4-24-4-4-42-2-24-24-422-4-2220000000000-2-2220000000000−2i32i3000000−2i3−2i32i32i3000000000000000000000000000000000000
χ5844-4-4-2440042-4-24-4-4-42-2-24-24-422-4-2220000000000-2-22200000000002i3−2i30000002i32i3−2i3−2i3000000000000000000000000000000000000
χ5944-4-4-24-20042-4-2-22-422-21-2-2-222-121-12000003i−3i3i−3i011-1-100003i−3i3i−3i00−2i32i30023−2300i3i3−i3−i3−3−33300000000000000000000000000000000
χ6044-4-4-24-20042-4-2-22-422-21-2-2-222-121-12000003i−3i3i−3i011-1-100003i−3i3i−3i002i3−2i300−232300−i3−i3i3i333−3−300000000000000000000000000000000
χ6144-4-4-24-20042-4-2-22-422-21-2-2-222-121-1200000−3i3i−3i3i011-1-10000−3i3i−3i3i00−2i32i300−232300i3i3−i3−i333−3−300000000000000000000000000000000
χ6244-4-4-24-20042-4-2-22-422-21-2-2-222-121-1200000−3i3i−3i3i011-1-10000−3i3i−3i3i002i3−2i30023−2300−i3−i3i3i3−3−33300000000000000000000000000000000
χ634-44-444-24-4-444-422-4-2-44-2-2-4224-2-222-44-4-4-22-2-2224-222-24-4-22-2-22200000000000000000000000000000000000000000000000000
χ644-44-444-2-44-444-422-4-2-44-2-2-4224-2-222-4-4442-222-2-2-4-222-2-442-222-2-200000000000000000000000000000000000000000000000000
χ654-44-44-244-424-2-4-4-424-4-24-2222-24-2-4-424-424-444-4-4-2-222-2-22-22-2-22200000000000000000000000000000000000000000000000000
χ664-44-44-2-24-424-2-4222-2-4-2-212-1-1-2-212224-42-22-2-222-21-1-11-221-111-1-10000000000000000000000003-3-330000000000000000000000
χ674-44-44-2-24-424-2-4222-2-4-2-212-1-1-2-212224-42-22-2-222-21-1-11-221-111-1-1000000000000000000000000-333-30000000000000000000000
χ684-44-44-2-2-4424-2-4222-2-4-2-212-1-1-2-21222-44-22-222-2-221-1-112-2-11-1-11100000000000000000000−2i32i300i3−i3i3−i30000000000000000000000
χ694-44-44-2-2-4424-2-4222-2-4-2-212-1-1-2-21222-44-22-222-2-221-1-112-2-11-1-111000000000000000000002i3−2i300−i3i3−i3i30000000000000000000000
χ704-44-4-2444-4-4-242-4-4-442-2-242-4-4-2-24222-22-44-4-2-2224-222-2-224-4-2-22200000000000000000000000000000000000000000000000000
χ714-44-4-244-44-4-242-4-4-442-2-242-4-4-2-242222-24-4422-2-2-4-222-22-2-4422-2-200000000000000000000000000000000000000000000000000
χ724-44-4-24-24-4-4-24222-4-22-21-2222-21-2-1-12-22-4-2211-1-141-1-11-22-2211-1-100000000003i−3i3i−3i3i−3i3i−3i00000000000000000000000000000000
χ734-44-4-24-24-4-4-24222-4-22-21-2222-21-2-1-12-22-4-2211-1-141-1-11-22-2211-1-10000000000−3i3i−3i3i−3i3i−3i3i00000000000000000000000000000000
χ744-44-4-24-2-44-4-24222-4-22-21-2222-21-2-1-122-242-2-1-111-41-1-112-22-2-1-11100000000003i−3i3i−3i−3i3i−3i3i00000000000000000000000000000000
χ754-44-4-24-2-44-4-24222-4-22-21-2222-21-2-1-122-242-2-1-111-41-1-112-22-2-1-1110000000000−3i3i−3i3i3i−3i3i−3i00000000000000000000000000000000
χ764-44-4-2-244-42-2-22-4-42421-2-2-1221-2-222-1-2224-4-2-222-21-1-111-1-2211-1-1000000000000000000000000000000003i−3i−3i3i00000000000000
χ774-44-4-2-244-42-2-22-4-42421-2-2-1221-2-222-1-2224-4-2-222-21-1-111-1-2211-1-100000000000000000000000000000000−3i3i3i−3i00000000000000
χ784-44-4-2-24-442-2-22-4-42421-2-2-1221-2-222-12-2-2-4422-2-221-1-11-112-2-1-111000000000000000000000000000023−2300−33−3300000000000000
χ794-44-4-2-24-442-2-22-4-42421-2-2-1221-2-222-12-2-2-4422-2-221-1-11-112-2-1-1110000000000000000000000000000−2323003−33−300000000000000
χ804-4-4444400-4-4-4-4-444-44444-4-44-4-4-4-44400000000004-44-40000000000000000000000000000000000000000000000000000000000
χ814-4-4444-200-4-4-4-42-24244-2-2-42-2-4222-240000000000-22-2200000000000023−23000023−23−2323000000000000000000000000000000000000
χ824-4-4444-200-4-4-4-42-24244-2-2-42-2-4222-240000000000-22-22000000000000−23230000−232323−23000000000000000000000000000000000000
χ834-4-444-24002-42-4-44-2-44-24-222-22-42-44-20000000000-22-220000000000000000000000000000000000000000000000i6−i6−i6i600000000
χ844-4-444-24002-42-4-44-2-44-24-222-22-42-44-20000000000-22-220000000000000000000000000000000000000000000000−i6i6i6−i600000000
χ854-4-44-24400-42-42-444-4-2-2-242-4422-42-2-20000000000-22-220000000000000000−2i32i30000−2i32i32i3−2i300000000000000000000000000000000
χ864-4-44-24400-42-42-444-4-2-2-242-4422-42-2-20000000000-22-2200000000000000002i3−2i300002i3−2i3−2i32i300000000000000000000000000000000
χ874-4-44-24-200-42-422-242-2-21-222-22-12-11-2000003i−3i−3i3i01-11-100003i−3i−3i3i000023−23002i3−2i3−333−3−i3i3i3−i300000000000000000000000000000000
χ884-4-44-24-200-42-422-242-2-21-222-22-12-11-2000003i−3i−3i3i01-11-100003i−3i−3i3i0000−232300−2i32i33−3−33i3−i3−i3i300000000000000000000000000000000
χ894-4-44-24-200-42-422-242-2-21-222-22-12-11-200000−3i3i3i−3i01-11-10000−3i3i3i−3i000023−2300−2i32i3−333−3i3−i3−i3i300000000000000000000000000000000
χ904-4-44-24-200-42-422-242-2-21-222-22-12-11-200000−3i3i3i−3i01-11-10000−3i3i3i−3i0000−2323002i3−2i33−3−33−i3i3i3−i300000000000000000000000000000000
χ918888-4-4-488-4-4-4-4-4-4-4-4-4222222222222-4-4-4-4-42222-4-1-1-1-12222-1-1-1-100000000000000000000000000000000000000000000000000
χ928888-4-4-4-8-8-4-4-4-4-4-4-4-4-422222222222244444-2-2-2-24-1-1-1-1-2-2-2-2111100000000000000000000000000000000000000000000000000
χ9388-8-88-4-400-4-848-4444-8-4-42-42-244-2-444000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4800-444-48-84-842-4-42-44-244-44-2000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-400-444-4-4444422222-2-2-2-22-2-2000006i−6i6i−6i0-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-400-444-4-4444422222-2-2-2-22-2-200000−6i6i−6i6i0-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000
χ978-88-8-4-4-48-84-4-44444-44222-2-2-2222-2-2-2-444-4422-2-2-4-111-12-22-2-1-11100000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-884-4-44444-44222-2-2-2222-2-2-24-4-44-4-2-2224-111-1-22-2211-1-100000000000000000000000000000000000000000000000000
χ998-8-888-4-4004-84-84-4-448-4-424-2244-24-4-400000000002-22-20000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48004444-88-4-8-42-4-4-24-4-2444-4200000000002-22-20000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-40044444-4-44-4222-2-22-2-2-2-222000006i−6i−6i6i0-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-40044444-4-44-4222-2-22-2-2-2-22200000−6i6i6i−6i0-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000

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