Finite Group Databasebeta

← Group #13171589

Character table — Group #13171589

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112222222444444444444666666888888888881212121212121212121212121212121212121212121616161618181818242424242424242424242424243636363636363636363648727272108108
order12333466623336666612121222441212366666661212122446666666681212121212121224246661224886666121212121212242424222666812242412662428
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-111111111-11111111-1-1111111-1-11111-11-1111-1-1-11-1-1111-11-1-1-1-1-1-1-1-1
χ31111111111111111111111-11-11111111111111-1111-11-1-1-1-1-11-1111-111111111-1-111-11-1-1111-111111-11-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111-11-11111111111111-11-11-11-1-1-1-1-1-1-1111-111-1-11111-1-1-1-1-11-1-1-11-1-111-1-1-1-1-11-1-1-11-1-1-1-1-11111
χ5111111111111111111111-11-11-1-1111111111111-11-11-11111111-1-1-11-1-1111111-1-1-1-11-1111-111-1-1111-1-11-1-1-11-1-1-11-111-1-1
χ6111111111111111111111-11-11-1-1111111111111-1-1-11-111111-11-1-1-11-1-1-1-11111-1-1111-111-1-1-11-1-1-1-1-1-11-1-1-1-1-1-111-11-1-111
χ7111111111111111111111-1-1-1-1-1-111111111111-1-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111111111-1-1-1-1-1-11-11-1-1-11111-1-1111-11-1-11-1-1-111
χ8111111111111111111111-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1111-1-1
χ9111111111-1111-1-11111111111111-1-1-1-1-1-11111-1-111111-1-111-111-1-1111-1-1-1-1-1111-1-1-11-1-11-111-1-1-1-1-1-1111-1-1-11-1-1111-11-1
χ10111111111-1111-1-11111111111111-1-1-1-1-1-11111-1-1-11111-1-111111-1-111111-1-1-111111-11-1-1-1-1-11-1-1111-1-1-11-1-11111-1-1-11-11
χ11111111111-1111-1-11111111-11-1111-1-1-1-1-1-111111-111-11-111-1-1-1-11-1-1-111-1-1-1-1-11-1-1-1-111111-11-1-1-1-1-1-111-1-1111-1-1-111-11-11
χ12111111111-1111-1-11111111-11-1111-1-1-1-1-1-111111-1-11-11-111-1-11-11-1-1-11111-1-1-11-1-1111111-1-1-1-1-1-11111-11-111-1-111-1-11-11-1
χ13111111111-1111-1-1111111-11-11-1-11-1-1-1-1-1-11111-111-11-11-1-111-11-1111-1-1-1-1-1-1-11-1-111-1-1-1-1111111-1-1-11-11-111-1-1111-11-1-11
χ14111111111-1111-1-1111111-11-11-1-11-1-1-1-1-1-11111-11-1-11-11-1-11111-1111-1-111-1-1-11-1-1-1-1-1-1-1-1-11-111111111-1-1111-1-1-1-11-111-1
χ15111111111-1111-1-1111111-1-1-1-1-1-11-1-1-1-1-1-11111111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-1111111-111111-111-1-1-1-1-1-11-1-111111-1-111-1
χ16111111111-1111-1-1111111-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-111-1-11-1-111-1-1-111-1-1-1111-1-11-111-11-1-111111-1111-1-1-11-1-1-111-1-11
χ1722222-2222022200222-2-2-222-2-2-2-220000002-2-2-2000222200220-2-200-2-2-200000-2-22000200000-200000000-2000200000000
χ1822222-2222022200222-2-2-22-2-22-2-220000002-2-2-20002-22-200-2-202-2002-2-200000-22-20002000002000000002000-200000000
χ1922222-2222022200222-2-2-2-222-22220000002-2-2-2000-22-2200220-2200-22200000-22-2000-200000-2000000002000-200000000
χ2022222-2222022200222-2-2-2-2-2222220000002-2-2-2000-2-2-2-200-2-20220022200000-2-22000-200000200000000-2000200000000
χ212222-1222-122-1-1-1-1-12-1-122222222-122-1-1-1-1-1-1-1222022-1-1-1-1-1-102-1-1-1-1-1-1002-1-1-122002-1-1-1020-1-1-1000200-1-1-10-100000000
χ222222-1222-122-1-1-1-1-12-1-1222-22-222-122-1-1-1-1-1-1-12-2202-2-1111110-2-1-1-11-1-1002-1-1-1-2-200-2-1110201-1-1000-2001110100000000
χ232222-1222-122-1-1-1-1-12-1-122-22-22-2-2-122-1-1-1-1-1-1-122-20-221-1-1-1-1-102111-111002-1-1-1-2-20021-1-10-20-111000-2001110100000000
χ242222-1222-122-1-1-1-1-12-1-122-2-2-2-2-2-2-122-1-1-1-1-1-1-12-2-20-2-21111110-2111111002-1-1-12200-21110-20111000200-1-1-10-100000000
χ252222-1222-1-22-1-111-12-1-122222222-1-2-21111-1-1-12-2-2022-1-111-1-102-111-1-1-100-211-12200-2-1110-20-111000-200-1110-100000000
χ262222-1222-1-22-1-111-12-1-1222-22-222-1-2-21111-1-1-122-202-2-11-1-1110-2-1111-1-100-211-1-2-2002-1-1-10-201110002001-1-10100000000
χ272222-1222-1-22-1-111-12-1-122-22-22-2-2-1-2-21111-1-1-12-220-221-111-1-1021-1-1-11100-211-1-2-200-2111020-1-1-10002001-1-10100000000
χ282222-1222-1-22-1-111-12-1-122-2-2-2-2-2-2-1-2-21111-1-1-12220-2-211-1-1110-21-1-111100-211-1220021-1-10201-1-1000-200-1110-100000000
χ292222-1-222-102-1-1−i3i3-12-11-2-222-2-2-2-2-100−i3i3−i3i3-111-200022-1-1−i3i3-1-10-21−i3i3111000−i3i31-22000-1−i3i30001−i3i30000001−i3i30-100000000
χ302222-1-222-102-1-1−i3i3-12-11-2-22-2-22-2-2-100−i3i3−i3i3-111-20002-2-11i3−i311021−i3i3-111000−i3i312-2000-1i3−i3000-1−i3i3000000-1i3−i30100000000
χ312222-1-222-102-1-1−i3i3-12-11-2-2-222-222-100−i3i3−i3i3-111-2000-221-1−i3i3-1-10-2-1i3−i31-1-1000−i3i312-20001−i3i30001i3−i3000000-1i3−i30100000000
χ322222-1-222-102-1-1−i3i3-12-11-2-2-2-22222-100−i3i3−i3i3-111-2000-2-211i3−i31102-1i3−i3-1-1-1000−i3i31-220001i3−i3000-1i3−i30000001−i3i30-100000000
χ332222-1-222-102-1-1i3−i3-12-11-2-222-2-2-2-2-100i3−i3i3−i3-111-200022-1-1i3−i3-1-10-21i3−i3111000i3−i31-22000-1i3−i30001i3−i30000001i3−i30-100000000
χ342222-1-222-102-1-1i3−i3-12-11-2-22-2-22-2-2-100i3−i3i3−i3-111-20002-2-11−i3i311021i3−i3-111000i3−i312-2000-1−i3i3000-1i3−i3000000-1−i3i30100000000
χ352222-1-222-102-1-1i3−i3-12-11-2-2-222-222-100i3−i3i3−i3-111-2000-221-1i3−i3-1-10-2-1−i3i31-1-1000i3−i312-20001i3−i30001−i3i3000000-1−i3i30100000000
χ362222-1-222-102-1-1i3−i3-12-11-2-2-2-22222-100i3−i3i3−i3-111-2000-2-211−i3i31102-1−i3i3-1-1-1000i3−i31-220001−i3i3000-1−i3i30000001i3−i30-100000000
χ37222-122-1222-12-122-1-122-12020200-12-122-1-1-1-12-12020-10222-1-12-100020022-1-1-1-10000-10-1-1-102-100-1-1-10020002000-10-1-100
χ38222-122-1222-12-122-1-122-12020200-12-122-1-1-1-12-120-20-10222-1-1-2-1000200-2-2-1-1-1-10000-10-1-110-2-10011100-2000-2000101100
χ39222-122-1222-12-122-1-122-120-20-200-12-122-1-1-1-12-1-202010-2-2-21121000-20022-1-1-1-100001011-102100-1-1-100-2000-2000-101100
χ40222-122-1222-12-122-1-122-120-20-200-12-122-1-1-1-12-1-20-2010-2-2-211-21000-200-2-2-1-1-1-10000101110-2100111002000200010-1-100
χ41222-122-122-2-12-1-2-2-1-122-12020200-1-21-2-211-1-12-1-2020-102-2-2-1-1-2-1000200-2-2111-100001011-102-100111002000-2000-10-1100
χ42222-122-122-2-12-1-2-2-1-122-12020200-1-21-2-211-1-12-1-20-20-102-2-2-1-12-100020022111-10000101110-2-100-1-1-100-20002000101-100
χ43222-122-122-2-12-1-2-2-1-122-120-20-200-1-21-2-211-1-12-1202010-22211-21000-200-2-2111-10000-10-1-1-10210011100-20002000-101-100
χ44222-122-122-2-12-1-2-2-1-122-120-20-200-1-21-2-211-1-12-120-2010-2221121000-20022111-10000-10-1-110-2100-1-1-1002000-200010-1100
χ4522-12222-122-1-12222-1-122-12020-1-1-1-12-1-122-12-1-1022-10200000202220-1-1-1-1-1-1-1-100220-1002-1-10-1-12-1-102000000-1-1-1-10000
χ4622-12222-122-1-12222-1-122-12020-1-1-1-12-1-122-12-1-102-2-10200000-202220-1-111-1-1-1-100-2-20-100-2-110-1-1-2110-200000011110000
χ4722-12222-122-1-12222-1-122-1-20-2011-1-12-1-122-12-1-10-2210-20000020-2-2-2011-1-1-1-1-1-100-2-2010021-10112-1-10-200000011-110000
χ4822-12222-122-1-12222-1-122-1-20-2011-1-12-1-122-12-1-10-2-210-200000-20-2-2-201111-1-1-1-100220100-211011-21102000000-1-11-10000
χ4922-12222-12-2-1-12-2-22-1-122-12020-1-1-11-211-2-2-12-1-10-22-10200000-202-2-20-1-111111-100-2-20-10021-1011-2110200000011-1-10000
χ5022-12222-12-2-1-12-2-22-1-122-12020-1-1-11-211-2-2-12-1-10-2-2-10200000202-2-20-1-1-1-1111-100220-100-2110112-1-10-2000000-1-1110000
χ5122-12222-12-2-1-12-2-22-1-122-1-20-2011-11-211-2-2-12-1-102210-200000-20-22201111111-1002201002-1-10-1-1-2110-2000000-1-1-110000
χ5222-12222-12-2-1-12-2-22-1-122-1-20-2011-11-211-2-2-12-1-102-210-20000020-222011-1-1111-100-2-20100-2-110-1-12-1-102000000111-10000
χ53444-24-4-2440-24-200-2-24-42-4040-400-2000000-22-420000-20400-2-202000-400000002000000000002000000000000000000000
χ54444-24-4-2440-24-200-2-24-42-40-40400-2000000-22-42000020-400220-200040000000200000000000-2000000000000000000000
χ55444-2-24-24-24-2-21-2-21-2-2-2-2404040014-2-2-21111-2-24000-20-2-2-2110-2000-20000-21110000-20110001000000000000000000000
χ56444-2-24-24-24-2-21-2-21-2-2-2-240-40-40014-2-2-21111-2-2-400020222-1-10200020000-2111000020-1-1000-1000000000000000000000
χ57444-2-24-24-2-4-2-21221-2-2-2-240404001-4222-1-111-2-2-4000-20-222110-2000-200002-1-11000020-1-10001000000000000000000000
χ58444-2-24-24-2-4-2-21221-2-2-2-240-40-4001-4222-1-111-2-24000202-2-2-1-102000200002-1-110000-2011000-1000000000000000000000
χ59444-2-2-4-24-20-2-21−2i32i31-2-222-4040-400100−2i32i3i3−i31-1220000-20-2−2i32i31102000200000i3−i3-1000000i3−i3000-1000000000000000000000
χ60444-2-2-4-24-20-2-21−2i32i31-2-222-40-40400100−2i32i3i3−i31-12200002022i3−2i3-1-10-2000-200000i3−i3-1000000−i3i30001000000000000000000000
χ61444-2-2-4-24-20-2-212i3−2i31-2-222-4040-4001002i3−2i3−i3i31-1220000-20-22i3−2i31102000200000−i3i3-1000000−i3i3000-1000000000000000000000
χ62444-2-2-4-24-20-2-212i3−2i31-2-222-40-404001002i3−2i3−i3i31-1220000202−2i32i3-1-10-2000-200000−i3i3-1000000i3−i30001000000000000000000000
χ6344-244-44-240-2-24004-2-2-4-4240-4022-2000000-2-422000-2040000000-40002200000200000-2000000000000000000000000000
χ6444-244-44-240-2-24004-2-2-4-42-4040-2-2-2000000-2-42200020-400000004000-2-2000002000002000000000000000000000000000
χ6544-24-244-2-24-21-2-2-2-2-21-24-24040-2-21-2411-2-21-21-2040-20-20000000-2-2-201100-2111000001000-200110000000000000000000
χ6644-24-244-2-24-21-2-2-2-2-21-24-2-40-40221-2411-2-21-21-20-4020200000002220-1-100-211100000-1000200-1-10000000000000000000
χ6744-24-244-2-2-4-21-222-2-21-24-24040-2-212-4-1-1221-21-20-40-20-20000000-222011002-1-11000001000200-1-10000000000000000000
χ6844-24-244-2-2-4-21-222-2-21-24-2-40-402212-4-1-1221-21-204020200000002-2-20-1-1002-1-1100000-1000-200110000000000000000000
χ6944-24-2-44-2-20-21-2−2i32i3-2-212-4240-4022100i3−i3−2i32i312-12000-20-200000002−2i32i30-1-1000i3−i3-1000001000000i3−i30000000000000000000
χ7044-24-2-44-2-20-21-2−2i32i3-2-212-42-4040-2-2100i3−i3−2i32i312-120002020000000-22i3−2i3011000i3−i3-100000-1000000−i3i30000000000000000000
χ7144-24-2-44-2-20-21-22i3−2i3-2-212-4240-4022100−i3i32i3−2i312-12000-20-2000000022i3−2i30-1-1000−i3i3-1000001000000−i3i30000000000000000000
χ7244-24-2-44-2-20-21-22i3−2i3-2-212-42-4040-2-2100−i3i32i3−2i312-120002020000000-2−2i32i3011000−i3i3-100000-1000000i3−i30000000000000000000
χ7344-2-244-2-2441-2-244-21-24-2-20000001-2-2-2-2-2-21-2-210040000000040000000-2-2111100000000-20-2000-2110000000000100000
χ7444-2-244-2-2441-2-244-21-24-2-20000001-2-2-2-2-2-21-2-2100-400000000-40000000221111000000002020002-1-10000000000-100000
χ7544-2-244-2-24-41-2-2-4-4-21-24-2-200000012222221-2-2100400000000-4000000022-1-1-1100000000-20-20002-1-10000000000100000
χ7644-2-244-2-24-41-2-2-4-4-21-24-2-200000012222221-2-2100-40000000040000000-2-2-1-1-1100000000202000-2110000000000-100000
χ774-44440-4-4-4044400-4-4-40000000004000000-400000000000000000000000000000022−2200000000000000000000022−22000000
χ784-44440-4-4-4044400-4-4-40000000004000000-4000000000000000000000000000000−2222000000000000000000000−2222000000
χ794-4-2440-42-40-2-2400-422000000023−23-200000020000000000000000000023−236−600000022−22000000000006−600000000−22000000
χ804-4-2440-42-40-2-2400-422000000023−23-200000020000000000000000000023−23−66000000−222200000000000−66000000002−2000000
χ814-4-2440-42-40-2-2400-4220000000−2323-2000000200000000000000000000−23236−6000000−2222000000000006−6000000002−2000000
χ824-4-2440-42-40-2-2400-4220000000−2323-2000000200000000000000000000−2323−6600000022−2200000000000−6600000000−22000000
χ8388-4-48-8-4-4802-4-400-42-4-8440000002000000244-2000000000000000000000000-2000000000000000000000000000000000
χ8488-4-4-48-4-4-48222-4-4222-4-4-4000000-1-4-42222-12220000000000000000000002-1-1-1000000000000000000000000000000000
χ8588-4-4-48-4-4-4-822244222-4-4-4000000-144-2-2-2-2-1222000000000000000000000-211-1000000000000000000000000000000000
χ8688-4-4-4-8-4-4-40222−4i34i3222444000000-1002i3−2i32i3−2i3-1-2-2-20000000000000000000000−i3i31000000000000000000000000000000000
χ8788-4-4-4-8-4-4-402224i3−4i3222444000000-100−2i32i3−2i32i3-1-2-2-20000000000000000000000i3−i31000000000000000000000000000000000
χ888-888-40-8-8408-4-4004-84000000000-400000040000000000000000000000000000000000000000000000000000000000000
χ898-88-4804-8-80-48-40044-8000000000-400000040000000000000000000000000000000000000000000000000000000000000
χ908-88-4-404-840-4-4200-2440000000002000000-20000000000006-600000000000000000000000000000000000000000000000
χ918-88-4-404-840-4-4200-2440000000002000000-2000000000000-6600000000000000000000000000000000000000000000000
χ928-8-48-40-8440-42-40044-2000000043−432000000-200000000000000000000−2323000000000000000000000000000000000000000
χ938-8-48-40-8440-42-40044-20000000−43432000000-20000000000000000000023−23000000000000000000000000000000000000000
χ948-8-4-48044-802-4-4004-240000000002000000-2000000000000000000000026−260000000000000000000−660000000000000000
χ958-8-4-48044-802-4-4004-240000000002000000-20000000000000000000000−262600000000000000000006−60000000000000000
χ9616-16-8-8-80888044400-4-4-4000000000-200000020000000000000000000000000000000000000000000000000000000000000

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