Finite Group Databasebeta

← Group #13171582

Character table — Group #13171582

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size112222222444444444444666666888888888881212121212121212121212121212121212121212121616161618181818242424242424242424242424243636363636363636363648727272108108
order1233346662333666661212122244663666666612121222466666668121212121212121224246661224886666661212121224242422266681224246662448
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-111111111-111111111-1-1111111-1-1-11-11111111-1-1-11-1-1111-11-1-1-1-1-1-1-1-1
χ31111111111111111111111-11-1111111111111111-1-1111-11111-11-1-1-1-1-1111111-1-111111-111-11-1-1111-11-1-1-1-1-1-1111-11-1-1-1
χ41111111111111111111111-11-111111111111111-1-1-1111-111-11-11-1-1-1-1-1-1-11111-1-1-1-1-11-1-111-11-1-1-1-1-1-1-11-1-1-11-1-1-1-11-1111
χ5111111111111111111111-11-11-1-111111111111-1111-1-1-11-1-11-11-111111111111-1-1-1-11-111-1-11-111111-1-11-1-1-11-1-1-111-11-1-1
χ6111111111111111111111-11-11-1-111111111111-1-111-1-1-11-1-1-1-11-111111-1-11111-1-111-1-1-11-1-11-111-1-1-1-11-1-1-1-1-1-111-1-11-111
χ7111111111111111111111-1-1-1-1-1-111111111111-11-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11-11-1-1-1-1-1-1-11111-1-1111-11-1-11-1-1-111
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
χ9111111111-1111-1-11111111111111-1-1-1-1-1-11111-11-111-1-1111-11111-1-111-1-1-1-1-1111-1-11-111-1-1-11-1-1-1-1-1-1111-1-1-11-1-1111-11-1
χ10111111111-1111-1-11111111111111-1-1-1-1-1-11111-1-1-111-1-111111111-1-11111-1-1-111111-1-1-11-1-1-11-1-1111-1-1-11-1-11111-1-1-11-11
χ11111111111-1111-1-11111111-11-1111-1-1-1-1-1-11111-111-11-1-1-111-11-11-111-1-1-1-1-1-1-11-1-1-1-11-11-1-1-11111-1-1-111-1-1111-1-1-11-111-11
χ12111111111-1111-1-11111111-11-1111-1-1-1-1-1-11111-1-11-11-1-1-11111-11-111-1-111-1-1-11-1-111-1-1-1-1-1-111111111-11-111-1-111-11-1-11-1
χ13111111111-1111-1-1111111-11-11-1-11-1-1-1-1-1-1111111-11-1111-1-1-1-11-11-1-111-1-1-1-1-11-1-111111111-1-1-1-1-1-1-11-11-111-1-11111-1-1-11
χ14111111111-1111-1-1111111-11-11-1-11-1-1-1-1-1-111111-1-11-1111-1-11-11-11-1-11111-1-1-11-1-1-1-1-11-1111-1-1-1-111111-1-1111-1-1-1-1-1111-1
χ15111111111-1111-1-1111111-1-1-1-1-1-11-1-1-1-1-1-11111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111-1111-111-1-1-1-1-1-11-1-111111-1-111-1
χ16111111111-1111-1-1111111-1-1-1-1-1-11-1-1-1-1-1-111111-11-1-111-1-1-11-1-1-1-111-1-111-1-1-1111-1-1-11-1-1111-111111-1111-1-1-11-1-1-111-1-11
χ1722222-2222022200222-2-2-222-2-22220000002-2-2-200022002220-2-2-2-200-2-200000-2-22000002000-200000000-2000200000000
χ1822222-2222022200222-2-2-22-2-222220000002-2-2-2000-2200-2220-22-22002200000-22-200000-2000-2000000002000-200000000
χ1922222-2222022200222-2-2-2-222-2-2-220000002-2-2-20002-2002-2-202-22-200-2-200000-22-20000020002000000002000-200000000
χ2022222-2222022200222-2-2-2-2-222-2-220000002-2-2-2000-2-200-2-2-202222002200000-2-2200000-2000200000000-2000200000000
χ212222-1222-12-12-1-1-12-1-1-122222222-122-1-1-1-1-1-1-122022-1-1-1-1-1-1022-1-1-1-1-1-1002-1-1-12200020-1-1-12-1-1-1000200-1-1-10-100000000
χ222222-1222-12-12-1-1-12-1-1-1222-22-222-122-1-1-1-1-1-1-1220-2-2-1-1-11-1-102-2-111111002-1-1-1-2-2000201-1-1-2-111000-2001110100000000
χ232222-1222-12-12-1-1-12-1-1-122-22-22-2-2-122-1-1-1-1-1-1-12-2022111-1110-221-1-1-1-1-1002-1-1-1-2-2000-20-11121-1-1000-2001110100000000
χ242222-1222-12-12-1-1-12-1-1-122-2-2-2-2-2-2-122-1-1-1-1-1-1-12-20-2-21111110-2-2111111002-1-1-122000-20111-2111000200-1-1-10-100000000
χ252222-1222-1-2-12-1112-1-1-122222222-1-2-21111-1-1-12-20-22-111-1-1-1022-1-111-1-100-211-122000-20-111-2-111000-200-1110-100000000
χ262222-1222-1-2-12-1112-1-1-1222-22-222-1-2-21111-1-1-12-202-2-1111-1-102-2-11-1-11100-211-1-2-2000-201112-1-1-10002001-1-10100000000
χ272222-1222-1-2-12-1112-1-1-122-22-22-2-2-1-2-21111-1-1-1220-221-1-1-1110-221-111-1-100-211-1-2-200020-1-1-1-21110002001-1-10100000000
χ282222-1222-1-2-12-1112-1-1-122-2-2-2-2-2-2-1-2-21111-1-1-12202-21-1-11110-2-211-1-11100-211-122000201-1-121-1-1000-200-1110-100000000
χ292222-1-222-10-12-1−i3i32-1-11-2-222-2-222-100−i3i3−i3i3-111-20002-1−i3i3-1-1-10-2-211−i3i311000−i3i31-2200000-1−i3i301−i3i30000001−i3i30-100000000
χ302222-1-222-10-12-1−i3i32-1-11-2-22-2-2222-100−i3i3−i3i3-111-2000-2-1−i3i31-1-10-221-1i3−i3-1-1000−i3i312-2000001−i3i301i3−i3000000-1i3−i30100000000
χ312222-1-222-10-12-1−i3i32-1-11-2-2-222-2-2-2-100−i3i3−i3i3-111-200021i3−i3-11102-2-11−i3i311000−i3i312-200000-1i3−i30-1−i3i3000000-1i3−i30100000000
χ322222-1-222-10-12-1−i3i32-1-11-2-2-2-222-2-2-100−i3i3−i3i3-111-2000-21i3−i3111022-1-1i3−i3-1-1000−i3i31-22000001i3−i30-1i3−i30000001−i3i30-100000000
χ332222-1-222-10-12-1i3−i32-1-11-2-222-2-222-100i3−i3i3−i3-111-20002-1i3−i3-1-1-10-2-211i3−i311000i3−i31-2200000-1i3−i301i3−i30000001i3−i30-100000000
χ342222-1-222-10-12-1i3−i32-1-11-2-22-2-2222-100i3−i3i3−i3-111-2000-2-1i3−i31-1-10-221-1−i3i3-1-1000i3−i312-2000001i3−i301−i3i3000000-1−i3i30100000000
χ352222-1-222-10-12-1i3−i32-1-11-2-2-222-2-2-2-100i3−i3i3−i3-111-200021−i3i3-11102-2-11i3−i311000i3−i312-200000-1−i3i30-1i3−i3000000-1−i3i30100000000
χ362222-1-222-10-12-1i3−i32-1-11-2-2-2-222-2-2-100i3−i3i3−i3-111-2000-21−i3i3111022-1-1−i3i3-1-1000i3−i31-22000001−i3i30-1−i3i30000001i3−i30-100000000
χ37222-122-12222-1-122-1-122-122020-1-1-12-122-1-1-1-12-122002220-1-12-10200000-1-1-1-1-1-100222-1-10-1-10-1002-1-102000000-1-1-10-1000
χ38222-122-12222-1-122-1-122-122020-1-1-12-122-1-1-1-12-12-2002220-1-1-2-1020000011-1-1-1-100-2-2-2-110-1-10-100-2110-200000011101000
χ39222-122-12222-1-122-1-122-12-20-2011-12-122-1-1-1-12-1-2200-2-2-2011210-200000-1-1-1-1-1-100-2-221-101101002-1-10-200000011-101000
χ40222-122-12222-1-122-1-122-12-20-2011-12-122-1-1-1-12-1-2-200-2-2-2011-210-20000011-1-1-1-10022-2110110100-21102000000-1-110-1000
χ41222-122-122-22-1-1-2-2-1-122-122020-1-1-1-21-2-211-1-12-1-22002-2-20-1-1-2-1020000011111-100-2-221-10110-100-2110200000011-10-1000
χ42222-122-122-22-1-1-2-2-1-122-122020-1-1-1-21-2-211-1-12-1-2-2002-2-20-1-12-10200000-1-1111-10022-2110110-1002-1-10-2000000-1-1101000
χ43222-122-122-22-1-1-2-2-1-122-12-20-2011-1-21-2-211-1-12-12200-222011-210-20000011111-100222-1-10-1-10100-2110-2000000-1-1-101000
χ44222-122-122-22-1-1-2-2-1-122-12-20-2011-1-21-2-211-1-12-12-200-222011210-200000-1-1111-100-2-2-2-110-1-101002-1-1020000001110-1000
χ4522-12222-122-1-1222-12-122-1020200-1-12-1-122-12-1-1022-100020020-10222-1-122-1-1-1-10000-102-100-10-1-1-1-1-10020002000-1-10-100
χ4622-12222-122-1-1222-12-122-1020200-1-12-1-122-12-1-10-22-1000200-20-10222-1-1-2-2-1-1-1-1000010-2-100-10-1-111100-2000-2000110100
χ4722-12222-122-1-1222-12-122-10-20-200-1-12-1-122-12-1-102-21000-2002010-2-2-21122-1-1-1-10000-1021001011-1-1-100-2000-2000-110100
χ4822-12222-122-1-1222-12-122-10-20-200-1-12-1-122-12-1-10-2-21000-200-2010-2-2-211-2-2-1-1-1-1000010-2100101111100200020001-10-100
χ4922-12222-12-2-1-12-2-2-12-122-1020200-11-211-2-2-12-1-102-2-1000200-20-102-2-2-1-1-2-2111-10000-102-1001011111002000-2000-1-10100
χ5022-12222-12-2-1-12-2-2-12-122-1020200-11-211-2-2-12-1-10-2-2-100020020-102-2-2-1-122111-1000010-2-1001011-1-1-100-20002000110-100
χ5122-12222-12-2-1-12-2-2-12-122-10-20-200-11-211-2-2-12-1-10221000-200-2010-22211-2-2111-10000-102100-10-1-111100-20002000-110-100
χ5222-12222-12-2-1-12-2-2-12-122-10-20-200-11-211-2-2-12-1-10-221000-2002010-2221122111-1000010-2100-10-1-1-1-1-1002000-20001-10100
χ53444-24-4-24404-2-200-2-24-42-440-40-2-2-2000000-22-4200004000-2-2020-400000000002000000000002000000000000000000000
χ54444-24-4-24404-2-200-2-24-42-4-404022-2000000-22-420000-4000220-2040000000000200000000000-2000000000000000000000
χ55444-2-24-24-24-2-21-2-2-21-2-2-244040-2-214-2-2-21111-2-24000-2-2-20110-20-20000000-211100000-2001101000000000000000000000
χ56444-2-24-24-24-2-21-2-2-21-2-2-24-40-402214-2-2-21111-2-2-40002220-1-102020000000-211100000200-1-10-1000000000000000000000
χ57444-2-24-24-2-4-2-2122-21-2-2-244040-2-21-4222-1-111-2-2-4000-2220110-20-200000002-1-1100000200-1-101000000000000000000000
χ58444-2-24-24-2-4-2-2122-21-2-2-24-40-40221-4222-1-111-2-240002-2-20-1-1020200000002-1-1100000-200110-1000000000000000000000
χ59444-2-2-4-24-20-2-21−2i32i3-21-222-440-40-2-2100−2i32i3i3−i31-1220000-2−2i32i3011020200000000i3−i3-100000000i3−i30-1000000000000000000000
χ60444-2-2-4-24-20-2-21−2i32i3-21-222-4-404022100−2i32i3i3−i31-122000022i3−2i30-1-10-20-200000000i3−i3-100000000−i3i301000000000000000000000
χ61444-2-2-4-24-20-2-212i3−2i3-21-222-440-40-2-21002i3−2i3−i3i31-1220000-22i3−2i3011020200000000−i3i3-100000000−i3i30-1000000000000000000000
χ62444-2-2-4-24-20-2-212i3−2i3-21-222-4-4040221002i3−2i3−i3i31-12200002−2i32i30-1-10-20-200000000−i3i3-100000000i3−i301000000000000000000000
χ6344-244-44-240-2-2400-24-2-4-42040-400-2000000-2-422000-20004000020-400220000020000000-20000000000000000000000000
χ6444-244-44-240-2-2400-24-2-4-420-40400-2000000-2-4220002000-40000-20400-2-2000002000000020000000000000000000000000
χ6544-24-244-2-241-2-2-2-2-2-21-24-20404001-2411-2-21-21-2004-2000-20000-20-2-2-21100-21110000000100-20110000000000000000000
χ6644-24-244-2-241-2-2-2-2-2-21-24-20-40-4001-2411-2-21-21-200-420002000020222-1-100-21110000000-10020-1-10000000000000000000
χ6744-24-244-2-2-41-2-222-2-21-24-204040012-4-1-1221-21-200-4-2000-20000-20-22211002-1-11000000010020-1-10000000000000000000
χ6844-24-244-2-2-41-2-222-2-21-24-20-40-40012-4-1-1221-21-2004200020000202-2-2-1-1002-1-110000000-100-20110000000000000000000
χ6944-24-2-44-2-201-2-2−2i32i3-2-212-42040-400100i3−i3−2i32i312-12000-2000-20000202−2i32i3-1-1000i3−i3-1000000010000i3−i30000000000000000000
χ7044-24-2-44-2-201-2-2−2i32i3-2-212-420-40400100i3−i3−2i32i312-12000200020000-20-22i3−2i311000i3−i3-10000000-10000−i3i30000000000000000000
χ7144-24-2-44-2-201-2-22i3−2i3-2-212-42040-400100−i3i32i3−2i312-12000-2000-200002022i3−2i3-1-1000−i3i3-1000000010000−i3i30000000000000000000
χ7244-24-2-44-2-201-2-22i3−2i3-2-212-420-40400100−i3i32i3−2i312-12000200020000-20-2−2i32i311000−i3i3-10000000-10000i3−i30000000000000000000
χ7344-2-244-2-244-21-2441-2-24-2-20000001-2-2-2-2-2-21-2-210400000000400000000-2-211110000-20-20000000-2110000000000100000
χ7444-2-244-2-244-21-2441-2-24-2-20000001-2-2-2-2-2-21-2-210-400000000-400000000221111000020200000002-1-10000000000-100000
χ7544-2-244-2-24-4-21-2-4-41-2-24-2-200000012222221-2-210400000000-40000000022-1-1-110000-20-200000002-1-10000000000100000
χ7644-2-244-2-24-4-21-2-4-41-2-24-2-200000012222221-2-210-400000000400000000-2-2-1-1-1100002020000000-2110000000000-100000
χ774-44440-4-4-4044400-4-4-40000000004000000-400000000000000000000000000000022−2200000000000000000000022−22000000
χ784-44440-4-4-4044400-4-4-40000000004000000-4000000000000000000000000000000−2222000000000000000000000−2222000000
χ794-44-2402-4-404-2-20022-40000000−2i32i3-2000000200000000000−2i32i3000000000i6−i600000022−2200000000000i6−i600000000−22000000
χ804-44-2402-4-404-2-20022-40000000−2i32i3-2000000200000000000−2i32i3000000000−i6i6000000−222200000000000−i6i6000000002−2000000
χ814-44-2402-4-404-2-20022-400000002i3−2i3-20000002000000000002i3−2i3000000000i6−i6000000−222200000000000i6−i6000000002−2000000
χ824-44-2402-4-404-2-20022-400000002i3−2i3-20000002000000000002i3−2i3000000000−i6i600000022−2200000000000−i6i600000000−22000000
χ8388-4-48-8-4-480-42-4002-4-4-8440000002000000244-2000000000000000000000000-2000000000000000000000000000000000
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
χ888-888-40-8-840-48-400-844000000000-400000040000000000000000000000000000000000000000000000000000000000000
χ898-88-4-404-840-4-42004-240000000−4i34i32000000-2000000000002i3−2i3000000000000000000000000000000000000000000000000
χ908-88-4-404-840-4-42004-2400000004i3−4i32000000-200000000000−2i32i3000000000000000000000000000000000000000000000000
χ918-8-4880-84-80-4-48004-84000000000-400000040000000000000000000000000000000000000000000000000000000000000
χ928-8-48-40-84402-4-40044-20000000002000000-2000000000000000000006i−6i000000000000000000000000000000000000000
χ938-8-48-40-84402-4-40044-20000000002000000-200000000000000000000−6i6i000000000000000000000000000000000000000
χ948-8-4-48044-80-42-400-2440000000002000000-200000000000000000000002i6−2i60000000000000000000−i6i60000000000000000
χ958-8-4-48044-80-42-400-2440000000002000000-20000000000000000000000−2i62i60000000000000000000i6−i60000000000000000
χ9616-16-8-8-80888044400-4-4-4000000000-200000020000000000000000000000000000000000000000000000000000000000000

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