Finite Group Databasebeta

← Group #13171672

Character table — Group #13171672

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size112222222444444444466888888888812121212121212121212121616161616181824242424242424242424242424242424242727363636363636364848547272727272108
order1233346663334666121212243612121212121212124446666881212121212121224121212121212121212242424242424242444222688121212266624242
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-111111-11111111-1-1111-11-11111-11-111-1-1-1-11-1-1-11-1-11-1-11-1-11-1-1
χ311111111111111111111111111111111-111111-111111111-1-111-11-11111-11-11-1-111-1-1-11-1-1-11-1-11-1-11-1-11-1
χ411111111111111111111111111111111-1-11111-1-111111111111-1-1-1-1111-1-1-1-1-1-1-1-111-1-111-1-11-1-11-1-11-1-11
χ51111111111111111111-1-11111111111-111-1-1-1-111-1-11111111-1-11111-1-1-111111111-1-1-1-111-1-1111-1-1-11-1-1-1
χ61111111111111111111-1-11111111111-11-1-1-1-1-11-1-1-111111-1-1-1-11-11-1-1-1-11-11-111-1-111-11-1-1-11-11-11-11-1-111
χ71111111111111111111-1-11111111111-1-11-1-1-1-1-11-1-111111-1-1-1-1-11-11-1-1-1-11-11-1-111111-1-1-11-1-1-1111-1-11-11
χ81111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-111111-1
χ9111111111111-11111111111-1-1-11-1-111-1111111-1-111-1-11-1-111-1-111111-1-1-1-1-1-1-1-1-1-11111-11-1-1111111-1-1-1-1
χ10111111111111-11111111111-1-1-11-1-111-11-11111-1111-1-11-1-1-1-1-1-11-11-11-1-1-11-11-1-111-1-11-11-1-11-11-1-11-11-111
χ11111111111111-11111111111-1-1-11-1-111-1-1111111-111-1-11-1-1-1-1-1-1-11-111-1-11-11-111-1-1-1-1-111-11-1-1-11-1-1111-11
χ12111111111111-11111111111-1-1-11-1-111-1-1-111111111-1-11-1-111-1-1-1-1-1-11-1-11111111111-1-1-11111-1-11-1-1-111-1
χ13111111111111-1111111-1-111-1-1-11-1-111111-1-1-1-1-1-1-1-1-1-11-1-111111111-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111
χ14111111111111-1111111-1-111-1-1-11-1-11111-1-1-1-1-1-11-1-1-1-11-1-1-1-1111-11-1-111-11-11-1-11111-111-11-1-11-11-1111-1-1
χ15111111111111-1111111-1-111-1-1-11-1-1111-11-1-1-1-11-1-1-1-1-11-1-1-1-111-11-11-1111-11-111-1-1111-11-1-11-1-1111-11-11-1
χ16111111111111-1111111-1-111-1-1-11-1-1111-1-1-1-1-1-111-1-1-1-11-1-11111-1-1-1-1-11111111111-1-111-11-1-11-1-1-111-1-1-11
χ1722222-22222220222-2-2-22-222000-200-2-2000222200-2-200-2002-2000000-20000000000-2-2000200-2002000000
χ1822222-22222220222-2-2-22-222000-200-2-2000222200-2-200-200-22000000-2000000000022000-200200-2000000
χ1922222-22222220222-2-2-2-2222000-200-2-2000-2-2-2-2002200-2002-20000002000000000022000200-200-2000000
χ2022222-22222220222-2-2-2-2222000-200-2-2000-2-2-2-2002200-200-2200000020000000000-2-2000-2002002000000
χ212222-1222-1-1-122-1-12-12200-1-122-1222-1-102200002200-1-1-1-1-1220022-1-1000-1-122-1-1-1-100002-100-1-1-1000-1000
χ222222-1222-1-1-122-1-12-12200-1-122-1222-1-102-200002-200-1-1-1-1-1-2-2002-2-11000-112-2-1-1110000-21001-110001000
χ232222-1222-1-1-122-1-12-12200-1-122-1222-1-10-220000-2200-1-1-1-1-1-2-200-221-10001-1-2211-1-10000-210011-10001000
χ242222-1222-1-1-122-1-12-12200-1-122-1222-1-10-2-20000-2-200-1-1-1-1-12200-2-21100011-2-2111100002-100-111000-1000
χ252222-1222-1-1-12-2-1-12-12200-1-1-2-212-2-2-1-10220000-2-20011-111220022-1-100011-2-211110000-2-100-1-1-10001000
χ262222-1222-1-1-12-2-1-12-12200-1-1-2-212-2-2-1-102-20000-220011-111-2-2002-2-110001-1-2211-1-1000021001-11000-1000
χ272222-1222-1-1-12-2-1-12-12200-1-1-2-212-2-2-1-10-2200002-20011-111-2-200-221-1000-112-2-1-1110000210011-1000-1000
χ282222-1222-1-1-12-2-1-12-12200-1-1-2-212-2-2-1-10-2-20000220011-1112200-2-211000-1-122-1-1-1-10000-2-100-1110001000
χ29222-1222-122-1-122-1-122-122-1-12-12-1-1-12-12022-1-1-1022-12-1-1-1-1002-10-102-1-1-1020-100-1-10002000200-100-100-10
χ30222-1222-122-1-122-1-122-122-1-12-12-1-1-12-120-22-1-1-10-22-12-1-1-1-1002-1010-2-1-1-10-2010011000-2000-20010010010
χ31222-1222-122-1-122-1-122-1-2-2-1-12-12-1-1-12-1-202-211102-212-1-1-1-100-210-102111020-100-1-1000-2000-200-10010010
χ32222-1222-122-1-122-1-122-1-2-2-1-12-12-1-1-12-1-20-2-21110-2-212-1-1-1-100-21010-21110-20100110002000200100-100-10
χ33222-1222-122-1-1-22-1-122-122-1-1-21-2-1112-1-2022-1-1-10-22-1-21-11100-210-102-1110-20100110002000-200-100-10010
χ34222-1222-122-1-1-22-1-122-122-1-1-21-2-1112-1-20-22-1-1-1022-1-21-11100-21010-2-111020-100-1-1000-2000200100100-10
χ35222-1222-122-1-1-22-1-122-1-2-2-1-1-21-2-1112-1202-21110-2-21-21-111002-10-1021-1-10-2010011000-2000200-100100-10
χ36222-1222-122-1-1-22-1-122-1-2-2-1-1-21-2-1112-120-2-211102-21-21-111002-1010-21-1-1020-100-1-10002000-200100-10010
χ3722-1222-122-12-12-12-12-1222-1-1-122-1-1-1-12220-12-1-120-12-12-1-1-100-12-1020-1-1-120-10-1-100002000200-100-100-100
χ3822-1222-122-12-12-12-12-1222-1-1-122-1-1-1-122-20-12-1-1-20-12-12-1-1-100-1210-20-1-1-1-2010110000-2000-200100100100
χ3922-1222-122-12-12-12-12-12-2-2-1-1-122-1-1-1-12-2201-211201-2-12-1-1-1001-2-102011120-10-1-10000-2000-200-100100100
χ4022-1222-122-12-12-12-12-12-2-2-1-1-122-1-1-1-12-2-201-211-201-2-12-1-1-1001-210-20111-20101100002000200100-100-100
χ4122-1222-122-12-1-2-12-12-1222-1-11-2-2-111-12-220-12-1-1-20-121-2-111001-2-1020-111-20101100002000-200-100-100100
χ4222-1222-122-12-1-2-12-12-1222-1-11-2-2-111-12-2-20-12-1-120-121-2-111001-210-20-11120-10-1-10000-2000200100100-100
χ4322-1222-122-12-1-2-12-12-12-2-2-1-11-2-2-111-122201-211-201-21-2-11100-12-10201-1-1-2010110000-2000200-100100-100
χ4422-1222-122-12-1-2-12-12-12-2-2-1-11-2-2-111-122-201-211201-21-2-11100-1210-201-1-120-10-1-100002000-200100-100100
χ454444-2-444-2-2-240-2-242-4-400-2-2000-4002200000000000002004-40000000000000000000000-2002000000000
χ464444-2-444-2-2-240-2-242-4-400-2-2000-400220000000000000200-440000000000000000000000200-2000000000
χ47444-24-44-244-2-204-2-2-4-424-4-2-2000200-420004-2-2-200-42002000000000020000000000000000000000000000
χ48444-24-44-244-2-204-2-2-4-42-44-2-2000200-42000-4222004-20020000000000-20000000000000000000000000000
χ49444-2-244-2-2-21-24-21-2-24-200114-2-2-2-2-2-2100400000400-2111100000-20-20000-20-20011000000000010000000
χ50444-2-244-2-2-21-24-21-2-24-200114-2-2-2-2-2-2100-400000-400-2111100000202000020200-1-10000000000-10000000
χ51444-2-244-2-2-21-2-4-21-2-24-20011-422-222-2100400000-4002-11-1-100000-20-2000020200-1-1000000000010000000
χ52444-2-244-2-2-21-2-4-21-2-24-20011-422-222-2100-4000004002-11-1-1000002020000-20-200110000000000-10000000
χ5344-244-4-244-24-20-24-2-42-44-4-2-20002002-4000-24-2-2002-4002000000000020000000000000000000000000000
χ5444-244-4-244-24-20-24-2-42-4-44-2-20002002-40002-42200-240020000000000-20000000000000000000000000000
χ5544-24-24-24-21-2-241-2-2-2-240011-24-2-2-2-21-2040000040001-21110000-20-20000-20-201100000000000100000000
χ5644-24-24-24-21-2-241-2-2-2-240011-24-2-2-2-21-20-400000-40001-2111000020200002020-1-100000000000-100000000
χ5744-24-24-24-21-2-2-41-2-2-2-2400112-42-2221-20400000-4000-121-1-10000-20-200002020-1-100000000000100000000
χ5844-24-24-24-21-2-2-41-2-2-2-2400112-42-2221-20-4000004000-121-1-100002020000-20-201100000000000-100000000
χ5944-2-244-2-24-2-214-2-214-2-24411-2-24111-2-2400-2-21100-2-2-2-211100-2-2000011100000000000000000000000000
χ6044-2-244-2-24-2-214-2-214-2-2-4-411-2-24111-2-2-40022-1-10022-2-211100220000-1-1-100000000000000000000000000
χ6144-2-244-2-24-2-21-4-2-214-2-2441122-41-1-1-2-2-400-2-21100-2-2221-1-1002200001-1-100000000000000000000000000
χ6244-2-244-2-24-2-21-4-2-214-2-2-4-41122-41-1-1-2-240022-1-10022221-1-100-2-20000-11100000000000000000000000000
χ6344-2-24-4-2-24-2-210-2-21-4224-411000-13-322000-2-211002200-13-300000000-13-300000000000000000000000000
χ6444-2-24-4-2-24-2-210-2-21-4224-411000-1-3322000-2-211002200-1-3300000000-1-3300000000000000000000000000
χ6544-2-24-4-2-24-2-210-2-21-422-4411000-13-32200022-1-100-2-200-13-3000000001-3300000000000000000000000000
χ6644-2-24-4-2-24-2-210-2-21-422-4411000-1-332200022-1-100-2-200-1-330000000013-300000000000000000000000000
χ674-44440-4-4-44440-4-4-4000004-400000000000000000000000000000000000000000004i−4i0000000000000000
χ684-44440-4-4-44440-4-4-4000004-40000000000000000000000000000000000000000000−4i4i0000000000000000
χ69888-4-4-88-4-4-42-40-42-44-8400220004004-20000000000000-2000000000000000000000000000000000000000
χ7088-48-4-8-48-42-4-402-4-444-80022000400-240000000000000-2000000000000000000000000000000000000000
χ7188-4-4-48-4-4-42228222-4-4-400-1-1-4-4-4222220000000000022-1-1-10000000000000000000000000000000000000
χ7288-4-4-48-4-4-4222-8222-4-4-400-1-14442-2-22200000000000-2-2-1110000000000000000000000000000000000000
χ7388-4-4-4-8-4-4-4222022244400-1-1000-26-6-2-200000000000001-330000000000000000000000000000000000000
χ7488-4-4-4-8-4-4-4222022244400-1-1000-2-66-2-2000000000000013-30000000000000000000000000000000000000
χ758-888-40-8-84-4-48044-800000-440000000000000000000000000000000000000000000000000000000000000
χ768-88-480-84-88-4-40-84400000-440000000000000000000000000000000000000000000000000000000000000
χ778-88-4-40-844-42-404-24000002-20000000000000000000000000000000000000000032−32000000000000000000
χ788-88-4-40-844-42-404-24000002-200000000000000000000000000000000000000000−3232000000000000000000
χ798-8-48804-8-8-48-404-8400000-440000000000000000000000000000000000000000000000000000000000000
χ808-8-48-404-842-4-40-244000002-200000000000000000000000000000000000000032−3200000000000000000000
χ818-8-48-404-842-4-40-244000002-2000000000000000000000000000000000000000−323200000000000000000000
χ828-8-4-48044-8-4-42044-2000002-200000000000006-60000000000000000000000000000000000000000000000
χ838-8-4-48044-8-4-42044-2000002-20000000000000-660000000000000000000000000000000000000000000000
χ8416-16-8-8-808884440-4-4-400000-220000000000000000000000000000000000000000000000000000000000000

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