Finite Group Databasebeta

← Group #13171661

Character table — Group #13171661

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size1122222224444444444668888888888991212121212121212121212121212121616161616181818242424242424242424242424242424363636363636484854547272727272108
order12333466633346661212122436121212121212121244224668812121212242424241212121212212126666666121224242424242422468861224661224244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-11111111111-1-1111-1-1-1-1-1-1-1-11-1-11-1-1-1-1111-1-1-1-11
χ31111111111111111111111111111111-1-111-1111-1111111-1-111111-1-1-11111111-1-11-111-1-1-11-1-11-11-1-1-1-11-11-1-1
χ41111111111111111111111111111111-1-11-1111-111111-1-11111111-1-1-111-1-111111-11-1-111-1-11-1-11-11-1-1-1-11-11-1
χ51111111111111111111-1-1111111111111-111-1-111-1-1-1-1111111111111-1-111-1-1-1111111111-1-11-1-111-1-11-1-1-1-1-1
χ61111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111-1
χ71111111111111111111-1-11111111111-1-1-11-1-1-11-1-1-1-1-111-1-111111-1-1-1-1-111-1-1-1-1-11-111-1-1-1-11-1-111-111-1-11-111
χ81111111111111111111-1-11111111111-1-1-1-11-1-1-11-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-11-1-111-11-1-11-1-1111-11-11-11
χ9111111111111-11111111111-1-1-11-1-11111-11111-1-11111-1-1-1-1-1-11-1-1111-1-1111-1-111-1-1-1-1-1-1-1111-1-11111-111-1-1-1
χ10111111111111-11111111111-1-1-11-1-11111-1-1-1111111111111-1-11-1-1111-1-1-1-11-1-1-1-1111111-1-1-1111-1-111-1-1-111-1
χ11111111111111-11111111111-1-1-11-1-111-1-1-11-111-111111-1-111-1-11-1-1-1-1-1-1-1111-1-1-1-1-11-1-11111-1-1-111-1-1-111-1-111
χ12111111111111-11111111111-1-1-11-1-111-1-1-1-11111-1111111-1-1-1-11-1-1-1-1-1-1-1-1-11-1-1111-111-1-11-11-11-1-11-1-11-111-11
χ13111111111111-1111111-1-111-1-1-11-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111111-11111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1111
χ14111111111111-1111111-1-111-1-1-11-1-111111-1-1-1-111-1-1-1-11111-1-11-1-111111-1-1-111-1-1111111-1111-1-1-1-1-1-1-111-1-11
χ15111111111111-1111111-1-111-1-1-11-1-111-1-111-1-1-1-11-1-1-1-1-1-111-1-11-1-1-1-1-11111-111-1-1-11-1-1111-11-11-11-1111-111-1-1
χ16111111111111-1111111-1-111-1-1-11-1-111-1-11-11-1-11-1-1-1-1-111-1-1-1-11-1-1-1-1-111-1-1-111111-111-1-111-1-1-11-111111-1-11-1
χ1722222-22222220222-2-2-22-222000-200-2-2220002200-2-2-2-2000000-200-222000020000000000000-20000-22000000
χ1822222-22222220222-2-2-22-222000-200-2-2-2-20002200-2-2-2-2000000-2002-2-2000020000000000000200002-2000000
χ1922222-22222220222-2-2-2-2222000-200-2-222000-2-2002222000000-200-2220000-20000000000000-200002-2000000
χ2022222-22222220222-2-2-2-2222000-200-2-2-2-2000-2-2002222000000-2002-2-20000-2000000000000020000-22000000
χ212222-122-12-1-122-12-1-12200-1-12-12222-1-12202200220000-1-1-1-1-1-1-1-1-12-1-1002-1000-1222-1-1-1-1200-100-1-100-100000
χ222222-122-12-1-122-12-1-12200-1-12-12222-1-1220-2-200-2-200001111-1-1-1-1-12-1-100-210001-2-2-21111200-1001100-100000
χ232222-122-12-1-122-12-1-12200-1-12-12222-1-1-2-202-2002-20000-1-111-1-1-1-1-1-211002-10001-22-2-1-111-200100-1100100000
χ242222-122-12-1-122-12-1-12200-1-12-12222-1-1-2-20-2200-22000011-1-1-1-1-1-1-1-21100-21000-12-2211-1-1-2001001-100100000
χ252222-122-12-1-12-2-12-1-12200-1-1-21-22-2-2-1-12202200-2-20000111111-1112-1-1002-1000-12-2-21111-200-100-1-100100000
χ262222-122-12-1-12-2-12-1-12200-1-1-21-22-2-2-1-1220-2-200220000-1-1-1-111-1112-1-100-210001-222-1-1-1-1-200-1001100100000
χ272222-122-12-1-12-2-12-1-12200-1-1-21-22-2-2-1-1-2-202-200-22000011-1-111-111-211002-10001-2-2211-1-1200100-1100-100000
χ282222-122-12-1-12-2-12-1-12200-1-1-21-22-2-2-1-1-2-20-22002-20000-1-11111-111-21100-21000-122-2-1-1112001001-100-100000
χ29222-122-1222-1-12-1-122-1222-1-1-122-1-1-1-12002202-120-12-1-12200-12-1-1-10002-1-12-1-1-100-10-1-100020020-10000-10-100
χ30222-122-1222-1-12-1-122-1222-1-1-122-1-1-1-12002-202-1-20-12-1-1-2-200-12-1-1-10002-11-2-1-1-1001011000-200-201000010100
χ31222-122-1222-1-12-1-122-12-2-2-1-1-122-1-1-1-1200-220-21201-2112200-12-1-1-1000-21-1211100-10-1-1000-200-20-1000010100
χ32222-122-1222-1-12-1-122-12-2-2-1-1-122-1-1-1-1200-2-20-21-201-211-2-200-12-1-1-1000-211-21110010110002002010000-10-100
χ33222-122-1222-1-1-2-1-122-1222-1-11-2-2-111-1200-2202-1-20-12-1-1-2-2001-2-111000-21-12-111001011000200-20-10000-10100
χ34222-122-1222-1-1-2-1-122-1222-1-11-2-2-111-1200-2-202-120-12-1-122001-2-111000-211-2-11100-10-1-1000-200201000010-100
χ35222-122-1222-1-1-2-1-122-12-2-2-1-11-2-2-111-1200220-21-201-211-2-2001-2-1110002-1-121-1-1001011000-20020-1000010-100
χ36222-122-1222-1-1-2-1-122-12-2-2-1-11-2-2-111-12002-20-21201-21122001-2-1110002-11-21-1-100-10-1-1000200-2010000-10100
χ3722-122222-1-12-122-1-122-122-1-122-1-1-1-12-100202-12022-1-1-100222-1-1-1-1000-1200-1-1-12-10-100-1-10020020-10000-10-10
χ3822-122222-1-12-122-1-122-122-1-122-1-1-1-12-10020-2-120-22-1-1-100-2-22-1-1-1-1000-1200-1-1-1-2101001100-200-20100001010
χ3922-122222-1-12-122-1-122-1-2-2-1-122-1-1-1-12-100-2021-202-211100222-1-1-1-10001-2001112-10-100-1-100-200-20-100001010
χ4022-122222-1-12-122-1-122-1-2-2-1-122-1-1-1-12-100-20-21-20-2-211100-2-22-1-1-1-10001-200111-21010011002002010000-10-10
χ4122-122222-1-12-1-22-1-122-122-1-1-2-21-1112-100-202-120-22-1-1-100-2-2-21-1110001-200-1112-101001100200-20-10000-1010
χ4222-122222-1-12-1-22-1-122-122-1-1-2-21-1112-100-20-2-12022-1-1-10022-21-1110001-200-111-210-100-1-100-200201000010-10
χ4322-122222-1-12-1-22-1-122-1-2-2-1-1-2-21-1112-1002021-20-2-211100-2-2-21-111000-12001-1-12-101001100-20020-1000010-10
χ4422-122222-1-12-1-22-1-122-1-2-2-1-1-2-21-1112-10020-21-202-21110022-21-111000-12001-1-1-210-100-1-100200-2010000-1010
χ454444-2-44-24-2-240-24-22-4-400-2-2000-400224400000000000000000200-4-2-20000000000000000002000000000000
χ464444-2-44-24-2-240-24-22-4-400-2-2000-40022-4-400000000000000000200422000000000000000000-2000000000000
χ47444-24-4-2444-2-20-2-24-42-44-4-2-20002002-4000004-2002-4220000002000000000-200000000000000000000000000
χ48444-24-4-2444-2-20-2-24-42-4-44-2-20002002-400000-4200-24-2-20000002000000000200000000000000000000000000
χ49444-2-24-2-24-21-241-2-2-2-240011-2-24-2-2-21-20004000400000-2-2001-211100000-2-200000-2011000000001000000000
χ50444-2-24-2-24-21-241-2-2-2-240011-2-24-2-2-21-2000-4000-40000022001-211100000220000020-1-100000000-1000000000
χ51444-2-24-2-24-21-2-41-2-2-2-24001122-4-2221-20004000-4000002200-121-1-100000-2-20000020-1-1000000001000000000
χ52444-2-24-2-24-21-2-41-2-2-2-24001122-4-2221-2000-4000400000-2-200-121-1-1000002200000-201100000000-1000000000
χ5344-244-444-2-24-204-2-2-4-424-4-2-2000200-4200000-2400-42220000002000000000-200000000000000000000000000
χ5444-244-444-2-24-204-2-2-4-42-44-2-2000200-42000002-4004-2-2-20000002000000000200000000000000000000000000
χ5544-24-244-2-21-2-24-2-21-24-200114-2-2-2-2-2-21000040004000000-2-2-211110000000000-2-20-200110000000100000000
χ5644-24-244-2-21-2-24-2-21-24-200114-2-2-2-2-2-210000-4000-400000022-211110000000000220200-1-10000000-100000000
χ5744-24-244-2-21-2-2-4-2-21-24-20011-422-222-2100004000-4000000222-11-1-10000000000-2-20200-1-10000000100000000
χ5844-24-244-2-21-2-2-4-2-21-24-20011-422-222-210000-40004000000-2-22-11-1-10000000000220-200110000000-100000000
χ5944-2-244-24-2-2-214-21-24-2-24411-24-2111-2-200400-2-200-2-2110000-2-2111000-2-200111000000000000000000000000
χ6044-2-244-24-2-2-214-21-24-2-2-4-411-24-2111-2-200-400220022-1-10000-2-21110002200-1-1-1000000000000000000000000
χ6144-2-244-24-2-2-21-4-21-24-2-244112-421-1-1-2-200-400-2-200-2-2110000221-1-100022001-1-1000000000000000000000000
χ6244-2-244-24-2-2-21-4-21-24-2-2-4-4112-421-1-1-2-200400220022-1-10000221-1-1000-2-200-111000000000000000000000000
χ6344-2-24-4-24-2-2-210-21-2-4224-411000-13-32200000-2-20022-1-1000000-13-3000000013-3000000000000000000000000
χ6444-2-24-4-24-2-2-210-21-2-4224-411000-1-332200000-2-20022-1-1000000-1-3300000001-33000000000000000000000000
χ6544-2-24-4-24-2-2-210-21-2-422-4411000-13-322000002200-2-211000000-13-30000000-1-33000000000000000000000000
χ6644-2-24-4-24-2-2-210-21-2-422-4411000-1-3322000002200-2-211000000-1-330000000-13-3000000000000000000000000
χ674-44440-4-4-44440-4-4-4000004-4000000004i−4i0000000000000000000004i−4i0000000000000000000000000000000
χ684-44440-4-4-44440-4-4-4000004-400000000−4i4i000000000000000000000−4i4i0000000000000000000000000000000
χ694-444-20-42-4-2-2402-4200000-22000000004i−4i000000000006−6i6−i6000000−2i2i000000000006−6i6−i60000000000000000
χ704-444-20-42-4-2-2402-4200000-22000000004i−4i00000000000−66−i6i6000000−2i2i00000000000−66−i6i60000000000000000
χ714-444-20-42-4-2-2402-4200000-2200000000−4i4i000000000006−6−i6i60000002i−2i000000000006−6−i6i60000000000000000
χ724-444-20-42-4-2-2402-4200000-2200000000−4i4i00000000000−66i6−i60000002i−2i00000000000−66i6−i60000000000000000
χ73888-4-4-8-4-48-42-402-4-444-80022000400-240000000000000000000-2000000000000000000000000000000000000
χ7488-48-4-88-4-42-4-40-4-424-8400220004004-20000000000000000000-2000000000000000000000000000000000000
χ7588-4-4-48-4-4-42228222-4-4-400-1-1-4-4-4222220000000000000000022-1-1-10000000000000000000000000000000000
χ7688-4-4-48-4-4-4222-8222-4-4-400-1-14442-2-22200000000000000000-2-2-1110000000000000000000000000000000000
χ7788-4-4-4-8-4-4-4222022244400-1-1000-26-6-2-200000000000000000001-330000000000000000000000000000000000
χ7888-4-4-4-8-4-4-4222022244400-1-1000-2-66-2-2000000000000000000013-30000000000000000000000000000000000
χ798-88-4804-8-88-4-4044-800000-440000000000000000000000000000000000000000000000000000000000000000
χ808-88-4-4044-8-42-40-244000002-200000000000000000000026−26000000000000000000000−66000000000000000000
χ818-88-4-4044-8-42-40-244000002-2000000000000000000000−26260000000000000000000006−6000000000000000000
χ828-8-4880-8-84-48-40-84400000-440000000000000000000000000000000000000000000000000000000000000000
χ838-8-48-40-8442-4-4044-2000002-2000000000000000000000002i6−2i6000000000000000000000−i6i60000000000000000
χ848-8-48-40-8442-4-4044-2000002-200000000000000000000000−2i62i6000000000000000000000i6−i60000000000000000
χ858-8-4-4804-84-4-4204-24000002-200000000000000000006i−6i0000000000000000000000000000000000000000000
χ868-8-4-4804-84-4-4204-24000002-20000000000000000000−6i6i0000000000000000000000000000000000000000000
χ8716-16-8-8-808884440-4-4-400000-220000000000000000000000000000000000000000000000000000000000000000

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