Finite Group Databasebeta

← Group #13156568

Character table — Group #13156568

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222224444444444444444444444888888888888121212121212121212121212121212121212242424242424242424242424242424242424363636363636727272727272108108
order1222333446666666663336666666661212121212121212121236661212121212121212441212121212121212121212121212121244121212121212121212121212121212128824242424441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-11-1-111-1-1
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
χ61111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ71111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-11111-1-1-1-1-1-11-111-1-111
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
χ92222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-22-222-2-222-2-22222-2-2-2-200000000000000000000000000000000
χ102222222-2-2222222222222222222222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-22-2-222-2-222-2-2-2-2222200000000000000000000000000000000
χ11222222-12222-1-12222-12-1-12-1-12-1-1-12-1222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-102002200-1-10000-1-1-1-10000000200-1-100
χ12222222-12222-1-12222-12-1-12-1-12-1-1-12-1222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-10-200-2-20011000011110000000-2001100
χ13222222-12222-1-12222-12-1-12-1-12-1-1-12-1222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-2-21111-2-2-2-21111111102002200-1-10000-1-1-1-10000000-2001100
χ14222222-12222-1-12222-12-1-12-1-12-1-1-12-1222-1-1-1-1-1-12-1-1-1-122-1-1-1-1-1-1-2-21111-2-2-2-2111111110-200-2-20011000011110000000200-1-100
χ15222222-1-2-222-1-12222-12-1-12-1-12-1-1-12-1-2-2-2111111-2-1-1-1-1-2-21111112-2-1-11122-2-2-1-1-1-1111100000000−i3i30000−i3−i3i3i30000000000−i3i300
χ16222222-1-2-222-1-12222-12-1-12-1-12-1-1-12-1-2-2-2111111-2-1-1-1-1-2-21111112-2-1-11122-2-2-1-1-1-1111100000000i3−i30000i3i3−i3−i30000000000i3−i300
χ17222222-1-2-222-1-12222-12-1-12-1-12-1-1-12-1-2-2-2111111-2-1-1-1-1-2-2111111-2211-1-1-2-2221111-1-1-1-100000000−i3i30000−i3−i3i3i30000000000i3−i300
χ18222222-1-2-222-1-12222-12-1-12-1-12-1-1-12-1-2-2-2111111-2-1-1-1-1-2-2111111-2211-1-1-2-2221111-1-1-1-100000000i3−i30000i3i3−i3−i30000000000−i3i300
χ1922222-12222-12222-1-12-12-1-122-1-1-1-1-12-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1202200-1-100-1-1-1-1000000000020-1-10000
χ2022222-12222-12222-1-12-12-1-122-1-1-1-1-12-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-20-2-200110011110000000000-20110000
χ2122222-12222-12222-1-12-12-1-122-1-1-1-1-12-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2111111111111202200-1-100-1-1-1-10000000000-20110000
χ2222222-12222-12222-1-12-12-1-122-1-1-1-1-12-1-1222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-2-2-2-2-2111111111111-20-2-20011001111000000000020-1-10000
χ2322222-12-2-22-12222-1-12-12-1-122-1-1-1-1-1211-2-2-21111-2-1-1-1-111-2-211112-222-2-2-1-111-1-1-1-11111000000−i3i300−i3−i3i3i3000000000000−i3i30000
χ2422222-12-2-22-12222-1-12-12-1-122-1-1-1-1-1211-2-2-21111-2-1-1-1-111-2-211112-222-2-2-1-111-1-1-1-11111000000i3−i300i3i3−i3−i3000000000000i3−i30000
χ2522222-12-2-22-12222-1-12-12-1-122-1-1-1-1-1211-2-2-21111-2-1-1-1-111-2-21111-22-2-22211-1-11111-1-1-1-1000000−i3i300−i3−i3i3i3000000000000i3−i30000
χ2622222-12-2-22-12222-1-12-12-1-122-1-1-1-1-1211-2-2-21111-2-1-1-1-111-2-21111-22-2-22211-1-11111-1-1-1-1000000i3−i300i3i3−i3−i3000000000000−i3i30000
χ272222-12222-1222-1-1222-1-12-1-1-1-1222-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000022-1-1-1-12222-1-1-1-1-1-1-1-122-1-1-1-100000000
χ282222-12222-1222-1-1222-1-12-1-1-1-1222-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000002-2-1-11122-2-2-1-1-1-11111-2-2111100000000
χ292222-12222-1222-1-1222-1-12-1-1-1-1222-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2211-1-1-2-2221111-1-1-1-1-2-2111100000000
χ302222-12222-1222-1-1222-1-12-1-1-1-1222-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000-2-21111-2-2-2-21111111122-1-1-1-100000000
χ312-2-222222-2-22-2-2-22-2-22222-2-2-222-2-2-222-2-22-222-2-222-2-222-22-222-2-20000000000000000000000000000000000000000000000002i−2i
χ322-2-222222-2-22-2-2-22-2-22222-2-2-222-2-2-222-2-22-222-2-222-2-222-22-222-2-2000000000000000000000000000000000000000000000000−2i2i
χ332-2-22222-22-22-2-2-22-2-22222-2-2-222-2-2-22-222-22-2-222-22-2-22-22-22-2-2220000000000000000000000000000000000002i−2i2i2i−2i−2i00000000
χ342-2-22222-22-22-2-2-22-2-22222-2-2-222-2-2-22-222-22-2-222-22-2-22-22-22-2-222000000000000000000000000000000000000−2i2i−2i−2i2i2i00000000
χ352-2-22-122-2212-2-21-1-2-22-1-12111-12-2-21-1-22-1-22-2-2221-111-11-11-111-1-1000000000000000000003−3−i3i300003−33−3−i3i3−i3i32i−2i−i−iii00000000
χ362-2-22-122-2212-2-21-1-2-22-1-12111-12-2-21-1-22-1-22-2-2221-111-11-11-111-1-1000000000000000000003−3i3−i300003−33−3i3−i3i3−i3−2i2iii−i−i00000000
χ372-2-22-122-2212-2-21-1-2-22-1-12111-12-2-21-1-22-1-22-2-2221-111-11-11-111-1-100000000000000000000−33−i3i30000−33−33−i3i3−i3i3−2i2iii−i−i00000000
χ382-2-22-122-2212-2-21-1-2-22-1-12111-12-2-21-1-22-1-22-2-2221-111-11-11-111-1-100000000000000000000−33i3−i30000−33−33i3−i3i3−i32i−2i−i−iii00000000
χ3944444-2-2444-2-2-244-2-2-2-2-21-2-2-2-2111-2-2-2-24-2-2111141111-2-2-2-2111144-2-2-2-2-2-2-2-21111111100000000000000000000000000000000
χ4044444-2-2444-2-2-244-2-2-2-2-21-2-2-2-2111-2-2-2-24-2-2111141111-2-2-2-21111-4-422222222-1-1-1-1-1-1-1-100000000000000000000000000000000
χ4144444-2-2-4-44-2-2-244-2-2-2-2-21-2-2-2-2111-2-222-422-1-1-1-1-411112222-1-1-1-14-4-2-222-2-2221111-1-1-1-100000000000000000000000000000000
χ4244444-2-2-4-44-2-2-244-2-2-2-2-21-2-2-2-2111-2-222-422-1-1-1-1-411112222-1-1-1-1-4422-2-222-2-2-1-1-1-1111100000000000000000000000000000000
χ434444-244-4-4-2444-2-2444-2-24-2-2-2-2444-2-2-4-42-4-4-4-4-4-42-2-2-2-22222222200000000000000000000000000000000000000000000000000
χ444444-24-244-24-2-2-2-244-2-21-2-211-2-2-2-2-2144-2-2-2-2-2-2-2-21111-2-21111110000000000000000000400-2-200-2-20000111100000000000000
χ454444-24-244-24-2-2-2-244-2-21-2-211-2-2-2-2-2144-2-2-2-2-2-2-2-21111-2-21111110000000000000000000-4002200220000-1-1-1-100000000000000
χ464444-24-2-4-4-24-2-2-2-244-2-21-2-211-2-2-2-2-21-4-422222222111122-1-1-1-1-1-100000000000000000000000000−2i32i30000i3i3−i3−i300000000000000
χ474444-24-2-4-4-24-2-2-2-244-2-21-2-211-2-2-2-2-21-4-422222222111122-1-1-1-1-1-1000000000000000000000000002i3−2i30000−i3−i3i3i300000000000000
χ484444-2-2444-2-244-2-2-2-241-2-21-2-21-2-2-21-2-2-2-244-2-2-2-2-2111111-2-2111100000000000000000040-2-200-2-2001111000000000000000000
χ494444-2-2444-2-244-2-2-2-241-2-21-2-21-2-2-21-2-2-2-244-2-2-2-2-2111111-2-21111000000000000000000-4022002200-1-1-1-1000000000000000000
χ504444-2-24-4-4-2-244-2-2-2-241-2-21-2-21-2-2-21-2222-4-4222221111-1-122-1-1-1-1000000000000000000000000−2i32i300i3i3−i3−i3000000000000000000
χ514444-2-24-4-4-2-244-2-2-2-241-2-21-2-21-2-2-21-2222-4-4222221111-1-122-1-1-1-10000000000000000000000002i3−2i300−i3−i3i3i3000000000000000000
χ5244-4-444400-4-44-44-44-4-4444-44-4-4-44-44-4000000000044-4-40000000000000000000000000000000000000000000000000000000000
χ5344-4-444-200-4-4-224-44-424-2-2-4-22-42-22420000000000-2-2220000000000−2i32i3000000−2i3−2i32i32i3000000000000000000000000000000000000
χ5444-4-444-200-4-4-224-44-424-2-2-4-22-42-22420000000000-2-22200000000002i3−2i30000002i32i3−2i3−2i3000000000000000000000000000000000000
χ5544-4-44-2400-424-44-4-22-4-24-224-422-22-2-40000000000-2-222000000000000000023−2300002323−23−2300000000000000000000000000000000
χ5644-4-44-2400-424-44-4-22-4-24-224-422-22-2-40000000000-2-2220000000000000000−23230000−23−23232300000000000000000000000000000000
χ5744-4-44-2-200-42-224-4-222-2-212-222-11-1-22000003i−3i3i−3i011-1-100003i−3i3i−3i00−2i32i3000023−23i3i3−i3−i3−3−33300000000000000000000000000000000
χ5844-4-44-2-200-42-224-4-222-2-212-222-11-1-22000003i−3i3i−3i011-1-100003i−3i3i−3i002i3−2i30000−2323−i3−i3i3i333−3−300000000000000000000000000000000
χ5944-4-44-2-200-42-224-4-222-2-212-222-11-1-2200000−3i3i−3i3i011-1-10000−3i3i−3i3i00−2i32i30000−2323i3i3−i3−i333−3−300000000000000000000000000000000
χ6044-4-44-2-200-42-224-4-222-2-212-222-11-1-2200000−3i3i−3i3i011-1-10000−3i3i−3i3i002i3−2i3000023−23−i3−i3i3i3−3−33300000000000000000000000000000000
χ6144-4-4-244002-44-4-224-4-4-2-242-222-44-4-220000000000-2-22200000000000000000000000000000000000000000000006−66−600000000
χ6244-4-4-244002-44-4-224-4-4-2-242-222-44-4-220000000000-2-2220000000000000000000000000000000000000000000000−66−6600000000
χ634-44-4444004-4-44-4-4-44-44444-44-4-4-44-4-400000000004-44-40000000000000000000000000000000000000000000000000000000000
χ644-44-444-2004-42-2-4-4-4424-2-242-2-422-2-420000000000-22-22000000000000−2i32i300000000−2i32i3−2i32i300000000000000000000000000000000
χ654-44-444-2004-42-2-4-4-4424-2-242-2-422-2-420000000000-22-220000000000002i3−2i3000000002i3−2i32i3−2i300000000000000000000000000000000
χ664-44-44-240042-44-4-42-2-4-24-2-2-44222-22-40000000000-22-220000000000000023−230023−2323−23000000000000000000000000000000000000
χ674-44-44-240042-44-4-42-2-4-24-2-2-44222-22-40000000000-22-2200000000000000−232300−2323−2323000000000000000000000000000000000000
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χ694-44-44-2-200422-2-4-42-22-2-21-22-22-1-1122000003i−3i−3i3i01-11-100003i−3i−3i3i00002i3−2i3−2323003−33−3−i3i3−i3i300000000000000000000000000000000
χ704-44-44-2-200422-2-4-42-22-2-21-22-22-1-112200000−3i3i3i−3i01-11-10000−3i3i3i−3i0000−2i32i3−2323003−33−3i3−i3i3−i300000000000000000000000000000000
χ714-44-44-2-200422-2-4-42-22-2-21-22-22-1-112200000−3i3i3i−3i01-11-10000−3i3i3i−3i00002i3−2i323−2300−33−33−i3i3−i3i300000000000000000000000000000000
χ724-44-4-24400-2-4-4422-44-4-2-24-22-22-4-44220000000000-22-220000000000000000000000000000000000000000000000i6−i6−i6i600000000
χ734-44-4-24400-2-4-4422-44-4-2-24-22-22-4-44220000000000-22-220000000000000000000000000000000000000000000000−i6i6i6−i600000000
χ744-4-4444-24-4-4422-44-4-4-24-2-2-4224-222-4-24-4-4-22-2-2224-222-24-4-22-2-22200000000000000000000000000000000000000000000000000
χ754-4-4444-2-44-4422-44-4-4-24-2-2-4224-222-4-2-4442-222-2-2-4-222-2-442-222-2-200000000000000000000000000000000000000000000000000
χ764-4-444-244-4-4-2-4-4-44224-24-22-4-4-2-22224-22-44-4-2-2224-222-2-224-4-2-22200000000000000000000000000000000000000000000000000
χ774-4-444-24-44-4-2-4-4-44224-24-22-4-4-2-222242-24-4422-2-2-4-222-22-2-4422-2-200000000000000000000000000000000000000000000000000
χ784-4-444-2-24-4-4-222-4422-2-2-21222-21-1-12-2-22-4-2211-1-141-1-11-22-2211-1-100000000003i−3i−3i3i−3i3i3i−3i00000000000000000000000000000000
χ794-4-444-2-24-4-4-222-4422-2-2-21222-21-1-12-2-22-4-2211-1-141-1-11-22-2211-1-10000000000−3i3i3i−3i3i−3i−3i3i00000000000000000000000000000000
χ804-4-444-2-2-44-4-222-4422-2-2-21222-21-1-12-22-242-2-1-111-41-1-112-22-2-1-11100000000003i−3i−3i3i3i−3i−3i3i00000000000000000000000000000000
χ814-4-444-2-2-44-4-222-4422-2-2-21222-21-1-12-22-242-2-1-111-41-1-112-22-2-1-1110000000000−3i3i3i−3i−3i3i3i−3i00000000000000000000000000000000
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χ854-4-44-24-2-4424222-2-4-4-2-21-22-1-1-2-22221-44-22-222-2-221-1-112-2-11-1-1110000000000000000000000−2i32i300000000i3−i3i3−i300000000000000
χ864-4-44-24-2-4424222-2-4-4-2-21-22-1-1-2-22221-44-22-222-2-221-1-112-2-11-1-11100000000000000000000002i3−2i300000000−i3i3−i3i300000000000000
χ874-4-44-2-244-42-2-4-42-22241-2-2-1221-222-1-2-2224-4-2-222-21-1-111-1-2211-1-100000000000000000000000000003i−3i−3i3i000000000000000000
χ884-4-44-2-244-42-2-4-42-22241-2-2-1221-222-1-2-2224-4-2-222-21-1-111-1-2211-1-10000000000000000000000000000−3i3i3i−3i000000000000000000
χ894-4-44-2-24-442-2-4-42-22241-2-2-1221-222-1-22-2-2-4422-2-221-1-11-112-2-1-1110000000000000000000023−23000000−33−33000000000000000000
χ904-4-44-2-24-442-2-4-42-22241-2-2-1221-222-1-22-2-2-4422-2-221-1-11-112-2-1-11100000000000000000000−23230000003−33−3000000000000000000
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
χ9388-8-8-48-4004-8-44-448-84-42-442-244-44-4-2000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4800448-8-44-44-82-4-4-2-44-24-4424000000000022-2-20000000000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-40044-44-44-444222-22-2-2-22-22-2000006i−6i6i−6i0-1-1110000−3i3i−3i3i00000000000000000000000000000000000000000000000000
χ9688-8-8-4-4-40044-44-44-444222-22-2-2-22-22-200000−6i6i−6i6i0-1-11100003i−3i3i−3i00000000000000000000000000000000000000000000000000
χ978-88-8-48-400-4-84-444-884-42-4-4-22444-44-200000000002-22-20000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4800-44-88444-4-82-4-424-4-244-4-2400000000002-22-20000000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-400-444-4444-442222-22-2-2-22-2-2000006i−6i−6i6i0-11-110000−3i3i3i−3i00000000000000000000000000000000000000000000000000
χ1008-88-8-4-4-400-444-4444-442222-22-2-2-22-2-200000−6i6i6i−6i0-11-1100003i−3i−3i3i00000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-48-84-4444-444-4222-2-2-222-2-2-22-444-4422-2-2-4-111-12-22-2-1-11100000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-884-4444-444-4222-2-2-222-2-2-224-4-44-4-2-2224-111-1-22-2211-1-100000000000000000000000000000000000000000000000000

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