Finite Group Databasebeta

← Group #13171581

Character table — Group #13171581

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size11222222244444444444466666666668888888888812121212121212121212121212121212121212121216161616181824242424242424242424242436363636363636363636363636487272108108
order12333466623336666612121222446666883666666612121222266666666661212121224242424666122466666666121224242246881212122424242466648
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-11111111111111-111111111111111-1-1-1-111111111-1-1111111-1-1-1-111-1-1111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-11-111-1-111111111111111-11111-1-1-111-1-11-11-111111111-1-11-11111-1-11-1111-1-1-11-1-1-1-111-1-111-1-1-1
χ41111111111111111111111-11-111-1-1-1-1111111111111-1-1111-1-1-111-1-11-11-1-1-1-1-11111-1-11-1-1-111-1-11-1-1-1-11-1-1-11-1-1-1-1-111-1-1111
χ5111111111111111111111-11-11-1-1111111111111111-111-1-1-1111-1-111-11-1111111111-1-1-1111-1-111-1111-11-1-1-11-1-1-1-1-1111-11-1-1
χ6111111111111111111111-11-11-1-111-1-111111111111-11-1-1-1-1111-1-111-11-11-1-1-1-11111-1-1-11-1-1-1-111-11-1-11-1-1-11-1-1-1-111-1-1-11-111
χ7111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-111-1-111-1-1111-1-1-1-11-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-111-1-1
χ9111111111-1111-1-111111111111111111-1-1-1-1-1-11111-1-1-11-1-11-1-1111111111111-1-1-1111-1-1-1-1-1-1-1-11111-1-1-11111-1-11111-1-1-1-11
χ10111111111-1111-1-111111111111111-1-11-1-1-1-1-1-11111-1-111-1-11-1-111111111-1-1-1-1-1-1-1111-1-111-1-1-1-111-1-111-11-1-11-1-1-1-1-1-11111-1
χ11111111111-1111-1-11111111-11-111-1-1111-1-1-1-1-1-11111-11-11-1-1-11111-1-11-11-11111-1-1-11-1-1-11-1-1-1-1111-111-111-11-1-11111-1-1-1-111-1
χ12111111111-1111-1-11111111-11-111-1-1-1-11-1-1-1-1-1-11111-1111-1-1-11111-1-11-11-1-1-1-1-1-1-1-11-1-1-1111-1-1111-1-1-11-11-1-11-111-1-11111-1-11
χ13111111111-1111-1-1111111-11-11-1-111111-1-1-1-1-1-111111-1-1-1111-1-1-1-111-11-111111-1-1-11-1-11-1-1-111-1-1-11111-11-1-11-111-1-111-11-11-1
χ14111111111-1111-1-1111111-11-11-1-111-1-11-1-1-1-1-1-111111-11-1111-1-1-1-111-11-11-1-1-1-1-1-1-11-1-11-11111-1-1-11-1-1-111-11-1-11111-1-11-11-11
χ15111111111-1111-1-1111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-111-111-1-1-1-1-1-1-1-11111-1-1-111111-1-11111-1-11111-11-1-11-1-1-1-1-1-1-111-11
χ16111111111-1111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-11111-1-111111-1-11-1
χ1722222-2222022200222-2-2-222-2-222220020000002-2-2-20002002002222-2-2-2-20000000-2-2200000000-2-200000-200200000000000
χ1822222-2222022200222-2-2-22-2-2222-2-20020000002-2-2-2000200-20022-2-2-22-220000000-22-200000000-2200000200-200000000000
χ1922222-2222022200222-2-2-2-222-2-2-2220020000002-2-2-2000-200200-2-2222-22-20000000-22-2000000002-200000200-200000000000
χ2022222-2222022200222-2-2-2-2-222-2-2-2-20020000002-2-2-2000-200-200-2-2-2-222220000000-2-22000000002200000-200200000000000
χ212222-122-122-12-122-12-122-1020200-1-122-12-122-1-1-12-1-102200022200-1-10-10222-1-1-1-1-1-1000-12-100-1-10-1-1-102000200000-1-1-10-100
χ222222-122-122-12-122-12-122-1020200-1-1-2-2-12-122-1-1-12-1-102-200022200-1-10-102-2-211-1-1-1-1000-1-2100-1-10-1110-2000-2000001110100
χ232222-122-122-12-122-12-122-10-20-2001122-12-122-1-1-12-1-10-22000-2-2-20011010-222-1-1-1-1-1-100012-1001101-1-10-2000-20000011-10100
χ242222-122-122-12-122-12-122-10-20-20011-2-2-12-122-1-1-12-1-10-2-2000-2-2-20011010-2-2-211-1-1-1-10001-210011011102000200000-1-110-100
χ252222-122-12-2-12-1-2-2-12-122-1020200-1-122-1-21-2-211-12-1-10-2-20002-2-200-1-10-10222-1-1111-10001-2100110-1-1-10-2000200000-1-110100
χ262222-122-12-2-12-1-2-2-12-122-1020200-1-1-2-2-1-21-2-211-12-1-10-220002-2-200-1-10-102-2-211111-100012-100110-11102000-20000011-10-100
χ272222-122-12-2-12-1-2-2-12-122-10-20-2001122-1-21-2-211-12-1-102-2000-2220011010-222-1-1111-1000-1-2100-1-101-1-102000-2000001110-100
χ282222-122-12-2-12-1-2-2-12-122-10-20-20011-2-2-1-21-2-211-12-1-1022000-2220011010-2-2-211111-1000-12-100-1-101110-2000200000-1-1-10100
χ29222-122-1222-1-1222-1-122-122020-1-10022-1-12-1-122-1-12-1202222000-1-100-1020-1-122-1-1-1-100-10-12-1-100-10-1-1200020000-1-100-1-1000
χ30222-122-1222-1-1222-1-122-122020-1-100-2-2-1-12-1-122-1-12-120-2222000-1-100-102011-2-2-1-1-1-100-101-2-1-100-1011-2000-20000110011000
χ31222-122-1222-1-1222-1-122-12-20-20110022-1-12-1-122-1-12-1-202-2-2-2000110010-20-1-122-1-1-1-10010-12110010-1-1-2000-200001100-11000
χ32222-122-1222-1-1222-1-122-12-20-201100-2-2-1-12-1-122-1-12-1-20-2-2-2-2000110010-2011-2-2-1-1-1-100101-211001011200020000-1-1001-1000
χ33222-122-122-2-1-12-2-2-1-122-122020-1-10022-11-211-2-2-1-12-1-20-22-2-2000-1-100-1020-1-122111-100101-21100-10-1-1-200020000-1-10011000
χ34222-122-122-2-1-12-2-2-1-122-122020-1-100-2-2-11-211-2-2-1-12-1-2022-2-2000-1-100-102011-2-2111-10010-121100-10112000-200001100-1-1000
χ35222-122-122-2-1-12-2-2-1-122-12-20-20110022-11-211-2-2-1-12-120-2-222000110010-20-1-122111-100-101-2-1-10010-1-12000-2000011001-1000
χ36222-122-122-2-1-12-2-2-1-122-12-20-201100-2-2-11-211-2-2-1-12-1202-222000110010-2011-2-2111-100-10-12-1-1001011-200020000-1-100-11000
χ3722-122222-122-1-1-1-12-1-1-1222222222200-122-1-1-1-1-1-1-12220-1-1-1-1-1-1-1-1-1-122-1-100002-1-1-1222200-1-1-1-1-1-100002-100-1-1-1000000000
χ3822-122222-122-1-1-1-12-1-1-1222-22-222-2-200-122-1-1-1-1-1-1-122-20-1-1-1111-1-1112-2-1100002-1-1-1-2-22-200-1-111-110000-2100111000000000
χ3922-122222-122-1-1-1-12-1-1-122-22-22-2-22200-122-1-1-1-1-1-1-12-220111-1-1-111-1-1-221-100002-1-1-1-2-2-220011-1-11-10000-2100111000000000
χ4022-122222-122-1-1-1-12-1-1-122-2-2-2-2-2-2-2-200-122-1-1-1-1-1-1-12-2-201111111111-2-21100002-1-1-122-2-20011111100002-100-1-1-1000000000
χ4122-122222-1-22-1-1112-1-1-1222222222200-1-2-21111-1-1-12-2-20-111-111-1-1-1-122-1-10000-211-122-2-2001111-1-10000-2-100-111000000000
χ4222-122222-1-22-1-1112-1-1-1222-22-222-2-200-1-2-21111-1-1-12-220-1111-1-1-1-1112-2-110000-211-1-2-2-220011-1-1-11000021001-1-1000000000
χ4322-122222-1-22-1-1112-1-1-122-22-22-2-22200-1-2-21111-1-1-122-201-1-1-11111-1-1-221-10000-211-1-2-22-200-1-1111-1000021001-1-1000000000
χ4422-122222-1-22-1-1112-1-1-122-2-2-2-2-2-2-2-200-1-2-21111-1-1-122201-1-11-1-11111-2-2110000-211-1222200-1-1-1-1110000-2-100-111000000000
χ4522-122-222-102-1-1−i3i32-1-11-2-222-2-2222200-100−i3i3−i3i3-111-2000-1−i3i3-1−i3i3-1-1-1-1-2-21100000−i3i31-220000−i3i3−i3i31100000100-1−i3i3000000000
χ4622-122-222-102-1-1−i3i32-1-11-2-22-2-2222-2-200-100−i3i3−i3i3-111-2000-1−i3i31i3−i3-1-111-221-100000−i3i312-20000−i3i3i3−i31-100000-1001i3−i3000000000
χ4722-122-222-102-1-1−i3i32-1-11-2-2-222-2-2-22200-100−i3i3−i3i3-111-20001i3−i3-1−i3i311-1-12-2-1100000−i3i312-20000i3−i3−i3i3-1100000-1001i3−i3000000000
χ4822-122-222-102-1-1−i3i32-1-11-2-2-2-222-2-2-2-200-100−i3i3−i3i3-111-20001i3−i31i3−i3111122-1-100000−i3i31-220000i3−i3i3−i3-1-100000100-1−i3i3000000000
χ4922-122-222-102-1-1i3−i32-1-11-2-222-2-2222200-100i3−i3i3−i3-111-2000-1i3−i3-1i3−i3-1-1-1-1-2-21100000i3−i31-220000i3−i3i3−i31100000100-1i3−i3000000000
χ5022-122-222-102-1-1i3−i32-1-11-2-22-2-2222-2-200-100i3−i3i3−i3-111-2000-1i3−i31−i3i3-1-111-221-100000i3−i312-20000i3−i3−i3i31-100000-1001−i3i3000000000
χ5122-122-222-102-1-1i3−i32-1-11-2-2-222-2-2-22200-100i3−i3i3−i3-111-20001−i3i3-1i3−i311-1-12-2-1100000i3−i312-20000−i3i3i3−i3-1100000-1001−i3i3000000000
χ5222-122-222-102-1-1i3−i32-1-11-2-2-2-222-2-2-2-200-100i3−i3i3−i3-111-20001−i3i31−i3i3111122-1-100000i3−i31-220000−i3i3−i3i3-1-100000100-1i3−i3000000000
χ534444-2-44-240-24-200-24-2-4-42040-400-2-200-2000000-2-42200000040000-2-2020-40000000200000000000200000000000000000000
χ544444-2-44-240-24-200-24-2-4-420-404002200-2000000-2-422000000-40000220-2040000000200000000000-200000000000000000000
χ55444-24-4-2440-2-2400-2-24-42-440-40-2-20000-2000000-22-42000400000-2-20020-400000000200000000002000000000000000000000
χ56444-24-4-2440-2-2400-2-24-42-4-4040220000-2000000-22-42000-4000002200-2040000000020000000000-2000000000000000000000
χ57444-2-24-2-2441-2-2441-2-24-2-200000000441-2-2-2-2-2-21-2-2100400000000000000-2-2-2-211110000-2-200000011000000000000010000
χ58444-2-24-2-2441-2-2441-2-24-2-200000000-4-41-2-2-2-2-2-21-2-2100-40000000000000022221111000022000000-1-10000000000000-10000
χ59444-2-24-2-24-41-2-2-4-41-2-24-2-2000000004412222221-2-2100-400000000000000-2-2-2-2-1-1-11000022000000110000000000000-10000
χ60444-2-24-2-24-41-2-2-4-41-2-24-2-200000000-4-412222221-2-21004000000000000002222-1-1-110000-2-2000000-1-1000000000000010000
χ6144-24-244-2-24-2-21-2-2-2-21-24-2040400-2-20014-2-2-2111-21-2040000-2-2-200110-20-20000-2111000-20000110100000000000000000000
χ6244-24-244-2-24-2-21-2-2-2-21-24-20-40-400220014-2-2-2111-21-20-4000022200-1-102020000-211100020000-1-10-100000000000000000000
χ6344-24-244-2-2-4-2-2122-2-21-24-2040400-2-2001-4222-1-11-21-20-40000-22200110-20-200002-1-1100020000-1-10100000000000000000000
χ6444-24-244-2-2-4-2-2122-2-21-24-20-40-40022001-4222-1-11-21-20400002-2-200-1-1020200002-1-11000-20000110-100000000000000000000
χ6544-24-2-44-2-20-2-21−2i32i3-2-212-42040-400-2-200100−2i32i3i3−i312-12000000-2−2i32i30011020200000i3−i3-100000000i3−i30-100000000000000000000
χ6644-24-2-44-2-20-2-21−2i32i3-2-212-420-404002200100−2i32i3i3−i312-1200000022i3−2i300-1-10-20-200000i3−i3-100000000−i3i30100000000000000000000
χ6744-24-2-44-2-20-2-212i3−2i3-2-212-42040-400-2-2001002i3−2i3−i3i312-12000000-22i3−2i30011020200000−i3i3-100000000−i3i30-100000000000000000000
χ6844-24-2-44-2-20-2-212i3−2i3-2-212-420-4040022001002i3−2i3−i3i312-120000002−2i32i300-1-10-20-200000−i3i3-100000000i3−i30100000000000000000000
χ6944-2-244-24-24-21-2-2-2-21-2-2-244040-2-200001-2411-2-211-2-2400-2-2-20001100-20-200000-211100-200011001000000000000000000000
χ7044-2-244-24-24-21-2-2-2-21-2-2-24-40-402200001-2411-2-211-2-2-400222000-1-10020200000-2111002000-1-100-1000000000000000000000
χ7144-2-244-24-2-4-21-222-21-2-2-244040-2-2000012-4-1-12211-2-2-400-2220001100-20-2000002-1-11002000-1-1001000000000000000000000
χ7244-2-244-24-2-4-21-222-21-2-2-24-40-4022000012-4-1-12211-2-24002-2-2000-1-100202000002-1-1100-20001100-1000000000000000000000
χ7344-2-24-4-24-20-21-2−2i32i3-21-222-440-40-2-20000100i3−i3−2i32i31-122000-2−2i32i30001100202000000i3−i3-1000000i3−i300-1000000000000000000000
χ7444-2-24-4-24-20-21-2−2i32i3-21-222-4-4040220000100i3−i3−2i32i31-12200022i3−2i3000-1-100-20-2000000i3−i3-1000000−i3i3001000000000000000000000
χ7544-2-24-4-24-20-21-22i3−2i3-21-222-440-40-2-20000100−i3i32i3−2i31-122000-22i3−2i30001100202000000−i3i3-1000000−i3i300-1000000000000000000000
χ7644-2-24-4-24-20-21-22i3−2i3-21-222-4-4040220000100−i3i32i3−2i31-1220002−2i32i3000-1-100-20-2000000−i3i3-1000000i3−i3001000000000000000000000
χ774-44440-4-4-4044400-4-4-40000000000022−224000000-40000000000000000000022−2222−22000000000000000022−22000000000000000000
χ784-44440-4-4-4044400-4-4-400000000000−22224000000-400000000000000000000−2222−22220000000000000000−2222000000000000000000
χ794-444-20-42-40-24-2002-42000000000−2i32i322−22-2000000200000000000000−2i32i3000022−22−220000000000000000−2200000000000i6−i600000
χ804-444-20-42-40-24-2002-42000000000−2i32i3−2222-2000000200000000000000−2i32i30000−22222−200000000000000002−200000000000−i6i600000
χ814-444-20-42-40-24-2002-420000000002i3−2i322−22-20000002000000000000002i3−2i3000022−22−220000000000000000−2200000000000−i6i600000
χ824-444-20-42-40-24-2002-420000000002i3−2i3−2222-20000002000000000000002i3−2i30000−22222−200000000000000002−200000000000i6−i600000
χ834-44-2402-4-40-2-240022-40000000−2i32i30022−22-20000002000000000000−2i32i3000000−2222−220000000000000000−22000000000i6−i60000000
χ844-44-2402-4-40-2-240022-40000000−2i32i300−2222-20000002000000000000−2i32i30000002−2−222200000000000000002−2000000000−i6i60000000
χ854-44-2402-4-40-2-240022-400000002i3−2i30022−22-200000020000000000002i3−2i3000000−2222−220000000000000000−22000000000−i6i60000000
χ864-44-2402-4-40-2-240022-400000002i3−2i300−2222-200000020000000000002i3−2i30000002−2−222200000000000000002−2000000000i6−i60000000
χ87888-4-4-8-4-4802-4-4002-4-4-84400000000002000000244-2000000000000000000000000-200000000000000000000000000000000
χ8888-4-4-48-4-4-48222-4-4222-4-4-40000000000-1-4-42222-12220000000000000000000002-1-1-100000000000000000000000000000000
χ8988-4-4-48-4-4-4-822244222-4-4-40000000000-144-2-2-2-2-1222000000000000000000000-211-100000000000000000000000000000000
χ9088-4-4-4-8-4-4-40222−4i34i32224440000000000-1002i3−2i32i3−2i3-1-2-2-20000000000000000000000−i3i3100000000000000000000000000000000
χ9188-4-4-4-8-4-4-402224i3−4i32224440000000000-100−2i32i3−2i32i3-1-2-2-20000000000000000000000i3−i3100000000000000000000000000000000
χ928-88-4-4044-802-4-400-2440000000000042−422000000-200000000000000000000−2222−222200000000000000002−2000000000000000000
χ938-88-4-4044-802-4-400-24400000000000−42422000000-20000000000000000000022−2222−220000000000000000−22000000000000000000
χ948-8-4880-8-8408-4-400-8440000000000000-40000004000000000000000000000000000000000000000000000000000000000000
χ958-8-48-40-8440-4-420044-2000000000−4i34i3002000000-2000000000000002i3−2i300000000000000000000000000000000000000000000
χ968-8-48-40-8440-4-420044-20000000004i3−4i3002000000-200000000000000−2i32i300000000000000000000000000000000000000000000
χ978-8-4-4804-840-42-4004-240000000−4i34i300002000000-20000000000002i3−2i30000000000000000000000000000000000000000000000
χ988-8-4-4804-840-42-4004-2400000004i3−4i300002000000-2000000000000−2i32i30000000000000000000000000000000000000000000000
χ9916-16-8-8-80888044400-4-4-40000000000000-20000002000000000000000000000000000000000000000000000000000000000000

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