Finite Group Databasebeta

← Group #13167832

Character table — Group #13167832

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222222444444444444446688888888888888888812121212121212121218181818181824242424242424242424242424243636363636363648484848545472727272108
order12333466633366681212121212242424361212121224242424242424242424242422226681212246688666666666122424242422441224246666246612128
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111-1-111111-1-1-1-1-1-11111-1-1-1-11111111-11-1-1-1-111-1-1-1-11-11-1-1
χ31111111111111111111111111111111111111111111-1-11111111-1-1-1-1-1-1-1-1-1-11111111111-11-11-1-1-1-1-111-1-1-11-11-1
χ41111111111111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-1-1-111-1-1-1-11
χ511111111111111111111111-1-11111111111111111111111-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1
χ611111111111111111111111-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111-1-111-11-111
χ711111111111111111111111-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-1-1-1-1-1-111111-11-11
χ811111111111111111111111-1-1111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-11111-1
χ9111111111111111-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1111111-1-111-1-111-1-111-1-1-1-11-1-111-1-11-11-1111-1-11-1
χ10111111111111111-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1111-1-11-1-111-1-11
χ11111111111111111-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111-111-111-1-1-1-1-1111
χ12111111111111111-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1111111-1-1-1-111-1-11111-1-1-1-1-111-11-1-1-11-1111-111-1-1
χ13111111111111111-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-11-1-11111-1-111-1-111-1-1-1-11111-111-11-1-11-11-1-1-1-111-11
χ14111111111111111-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1111-1-1111-1-111-1
χ15111111111111111-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-1-1-1-1-111-1-11111-1-1-1-1111111-1-1-111-111-11111-1-1-1
χ16111111111111111-111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11-1-11111-1-1-1-111-1-111-1-111111-1-111-1-1-11-11-1-11-1-111
χ1722222-22222222220-2-2-2-2-2002-222-2-2-2-20000000000000000220-2-22-22200000000002-200000000-2000000-2200000
χ1822222-22222222220-2-2-2-2-2002-222-2-2-2-20000000000000000220-2-2-22-2-200000000002-20000000020000002-200000
χ1922222-22222222220-2-2-2-2-200-2222-2-2-2-20000000000000000-2-20222-2220000000000-2200000000-20000002-200000
χ2022222-22222222220-2-2-2-2-200-2222-2-2-2-20000000000000000-2-2022-22-2-20000000000-22000000002000000-2200000
χ212222-1222-1-12-12-1-122-1-1-122222-1-12-1-1-12-1-1-122-1-1-1-1-1-100222-122-100000000002-12-1-1-12-1-1-1020200000-1-1000-10-10
χ222222-1222-1-12-12-1-122-1-1-122222-1-12-1-1-12-1-1-122-1-1-1-1-1-100-2-22-122-10000000000-21-21-1-12-1-1-10-20-200000110001010
χ232222-1222-1-12-12-1-122-1-1-1222-2-2-1-12-1-1-12-1-1-122-1-1-1-1-1-10022-21-2-2100000000002-12-111-21110-20-200000-1-10001010
χ242222-1222-1-12-12-1-122-1-1-1222-2-2-1-12-1-1-12-1-1-122-1-1-1-1-1-100-2-2-21-2-210000000000-21-2111-211102020000011000-10-10
χ252222-1222-1-12-12-1-1-22-1-1-12-2-222-1-12-1-1-1-2111-2-2111111002-22-1-22-100000000002-1-21-1-1-21110-20200000-1100010-10
χ262222-1222-1-12-12-1-1-22-1-1-12-2-222-1-12-1-1-1-2111-2-211111100-222-1-22-10000000000-212-1-1-1-2111020-2000001-1000-1010
χ272222-1222-1-12-12-1-1-22-1-1-12-2-2-2-2-1-12-1-1-1-2111-2-2111111002-2-212-2100000000002-1-21112-1-1-1020-200000-11000-1010
χ282222-1222-1-12-12-1-1-22-1-1-12-2-2-2-2-1-12-1-1-1-2111-2-211111100-22-212-210000000000-212-1112-1-1-10-202000001-100010-10
χ29222-1222-12-1-12-12-12-12-1-122222-1-1-12-1-1-12-1-1-1-122-1-1-1-12200-122-120000002-12-10000-1-1-12-1-12020000-1-10000-10-100
χ30222-1222-12-1-12-12-12-12-1-122222-1-1-12-1-1-12-1-1-1-122-1-1-1-1-2-200-122-12000000-21-210000-1-1-12-1-1-20-2000011000010100
χ31222-1222-12-1-12-12-12-12-1-1222-2-2-1-1-12-1-1-12-1-1-1-122-1-1-1-122001-2-21-20000002-12-10000111-211-20-20000-1-1000010100
χ32222-1222-12-1-12-12-12-12-1-1222-2-2-1-1-12-1-1-12-1-1-1-122-1-1-1-1-2-2001-2-21-2000000-21-210000111-2112020000110000-10-100
χ33222-1222-12-1-12-12-1-2-12-1-12-2-222-1-1-12-1-11-21111-2-211112-200-12-2-120000002-1-210000-1-11-21120-20000-110000-10100
χ34222-1222-12-1-12-12-1-2-12-1-12-2-222-1-1-12-1-11-21111-2-21111-2200-12-2-12000000-212-10000-1-11-211-20200001-1000010-100
χ35222-1222-12-1-12-12-1-2-12-1-12-2-2-2-2-1-1-12-1-11-21111-2-211112-2001-221-20000002-1-21000011-12-1-1-2020000-11000010-100
χ36222-1222-12-1-12-12-1-2-12-1-12-2-2-2-2-1-1-12-1-11-21111-2-21111-22001-221-2000000-212-1000011-12-1-120-200001-10000-10100
χ3722-1222-1222-1-1-1-1222222-1-1-100-1-1-1-1-1-12222-1-1-1-1-1-1-1-122220000022-1-122-12-12-12-120000000000-1-1-1-1-1-1-10000000
χ3822-1222-1222-1-1-1-1222222-1-1-100-1-1-1-1-1-12222-1-1-1-1-1-1-1-122-2-200000-2-211-2-2-12-121-21-20000000000111-1-1110000000
χ3922-1222-1222-1-1-1-1222222-1-1-100-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-22200000-2-211-2-21-21-2-12-12000000000011111-1-10000000
χ4022-1222-1222-1-1-1-1222222-1-1-100-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-2-20000022-1-1221-21-21-21-20000000000-1-1-111110000000
χ4122-1222-1222-1-1-1-12-22222-11100-1-1-1-1-1-1-2-2-2-2111111112-22-20000022-1-1-2-2-121-2-121-20000000000-111-11-110000000
χ4222-1222-1222-1-1-1-12-22222-11100-1-1-1-1-1-1-2-2-2-2111111112-2-2200000-2-21122-121-21-2-1200000000001-1-1-111-10000000
χ4322-1222-1222-1-1-1-12-22222-11100-1-1-1-1-1-1-2-2-2-211111111-222-200000-2-211221-2-12-121-200000000001-1-11-1-110000000
χ4422-1222-1222-1-1-1-12-22222-11100-1-1-1-1-1-1-2-2-2-211111111-22-220000022-1-1-2-21-2-121-2-120000000000-1111-11-10000000
χ454444-2-444-2-24-24-2-20-4222-4004-4-2-2-422200000000000000004-20-4200000000000000-220000000000000000000000
χ464444-2-444-2-24-24-2-20-4222-400-44-2-2-42220000000000000000-4204-2000000000000002-20000000000000000000000
χ47444-24-44-24-2-24-24-202-422-4004-4-2-22-4220000000000000000-2402-400000000000000-220000000000000000000000
χ48444-24-44-24-2-24-24-202-422-400-44-2-22-42200000000000000002-40-24000000000000002-20000000000000000000000
χ49444-2-244-2-21-2-2-2-214-2-2114444411-2-211-2-211-2-2-2-211110000-2-24-2-20000000000000011-2-211000000000000000000
χ50444-2-244-2-21-2-2-2-214-2-211444-4-411-2-211-2-211-2-2-2-21111000022-42200000000000000-1-122-1-1000000000000000000
χ51444-2-244-2-21-2-2-2-21-4-2-2114-4-44411-2-21122-1-12222-1-1-1-10000-2-2-4-2-2000000000000001122-1-1000000000000000000
χ52444-2-244-2-21-2-2-2-21-4-2-2114-4-4-4-411-2-21122-1-12222-1-1-1-100002242200000000000000-1-1-2-211000000000000000000
χ53444-2-2-44-2-21-2-2-2-21022-1-1-4004-41122-1-1003i−3i00003i3i−3i−3i0000-2-2022000000000000001-1003i−3i000000000000000000
χ54444-2-2-44-2-21-2-2-2-21022-1-1-4004-41122-1-100−3i3i0000−3i−3i3i3i0000-2-2022000000000000001-100−3i3i000000000000000000
χ55444-2-2-44-2-21-2-2-2-21022-1-1-400-441122-1-1003i−3i00003i3i−3i−3i0000220-2-200000000000000-1100−3i3i000000000000000000
χ56444-2-2-44-2-21-2-2-2-21022-1-1-400-441122-1-100−3i3i0000−3i−3i3i3i0000220-2-200000000000000-11003i−3i000000000000000000
χ5744-244-4-2444-2-2-2-240-4-4-4-420000-2-222220000000000000000000004-4-2-20000000000000000000020000000000000
χ5844-244-4-2444-2-2-2-240-4-4-4-420000-2-22222000000000000000000000-442200000000000000000000-20000000000000
χ5944-24-24-24-2-2-21-21-244-2-2-2-2-2-20011-21114-2-2-2-2-21111110044000000000000000-2-2-2-2000000000000000110000000
χ6044-24-24-24-2-2-21-21-244-2-2-2-2-2-20011-21114-2-2-2-2-211111100-4-40000000000000002222000000000000000-1-10000000
χ6144-24-24-24-2-2-21-21-2-44-2-2-2-2220011-2111-422222-1-1-1-1-1-1004-4000000000000000-2-2220000000000000001-10000000
χ6244-24-24-24-2-2-21-21-2-44-2-2-2-2220011-2111-422222-1-1-1-1-1-100-4400000000000000022-2-2000000000000000-110000000
χ6344-2-244-2-24-21-21-2-24-24-2-2-2-2-200111-211-24-2-211-2-21111440000000000000-2-2-2-20000000000000000011000000000
χ6444-2-244-2-24-21-21-2-24-24-2-2-2-2-200111-211-24-2-211-2-21111-4-40000000000000222200000000000000000-1-1000000000
χ6544-2-244-2-24-21-21-2-2-4-24-2-2-22200111-2112-422-1-122-1-1-1-14-40000000000000-2-222000000000000000001-1000000000
χ6644-2-244-2-24-21-21-2-2-4-24-2-2-22200111-2112-422-1-122-1-1-1-1-44000000000000022-2-200000000000000000-11000000000
χ674-44440-4-4-4444-4-4-400000000004-40000000000000000000000000000022−22000000000000000000022−2200000000000
χ684-44440-4-4-4444-4-4-400000000004-400000000000000000000000000000−22220000000000000000000−222200000000000
χ694-4-24402-4-44-2-222-4000000i6−i600-2200000000i6−i6i6−i6i6−i6i6−i600000000000−2i32i322−220000000000000000000−2200000000000
χ704-4-24402-4-44-2-222-4000000i6−i600-2200000000i6−i6i6−i6i6−i6i6−i6000000000002i3−2i3−222200000000000000000002−200000000000
χ714-4-24402-4-44-2-222-4000000−i6i600-2200000000−i6i6−i6i6−i6i6−i6i600000000000−2i32i3−222200000000000000000002−200000000000
χ724-4-24402-4-44-2-222-4000000−i6i600-2200000000−i6i6−i6i6−i6i6−i6i6000000000002i3−2i322−220000000000000000000−2200000000000
χ7388-48-4-8-48-4-4-42-42-40-844440000224-2-2-200000000000000000000000000000000000000000000000000000000000
χ7488-4-48-8-4-48-42-42-4-404-8444000022-24-2-200000000000000000000000000000000000000000000000000000000000
χ7588-4-4-48-4-4-42222228-4-422-4-4-400-1-122-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000
χ7688-4-4-48-4-4-4222222-8-4-422-44400-1-122-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000
χ7788-4-4-4-8-4-4-4222222044-2-240000-1-1-2-211006i−6i0000−3i−3i3i3i00000000000000000000000000000000000000000000000
χ7888-4-4-4-8-4-4-4222222044-2-240000-1-1-2-21100−6i6i00003i3i−3i−3i00000000000000000000000000000000000000000000000
χ798-888-40-8-84-48-4-8440000000000-44000000000000000000000000000000000000000000000000000000000000000
χ808-88-480-84-8-4-484-840000000000-44000000000000000000000000000000000000000000000000000000000000000
χ818-88-4-40-8442-4-444-20006i−6i000002-2006i−6i00000000000000000000000000000000000000000000000000000000000
χ828-88-4-40-8442-4-444-2000−6i6i000002-200−6i6i00000000000000000000000000000000000000000000000000000000000
χ838-8-48-404-84-4-424-240000002i6−2i6002-2000000002i6−2i6−i6i6−i6i6−i6i600000000000000000000000000000000000000000000000
χ848-8-48-404-84-4-424-24000000−2i62i6002-200000000−2i62i6i6−i6i6−i6i6−i600000000000000000000000000000000000000000000000
χ858-8-4-48044-8-42-4-2440000002i6−2i6002-200000000−i6i62i6−2i6−i6i6−i6i600000000000000000000000000000000000000000000000
χ868-8-4-48044-8-42-4-244000000−2i62i6002-200000000i6−i6−2i62i6i6−i6i6−i600000000000000000000000000000000000000000000000
χ878-8-4-4-40444222-2-2-20006i−6i02i6−2i600-1100−3i3i0000−i6i6−i6i6−ζ5+2ζ7+ζ13−2ζ23ζ5−2ζ7−ζ13+2ζ232ζ5−ζ7−2ζ13+ζ23−2ζ5+ζ7+2ζ13−ζ2300000000000000000000000000000000000000000000000
χ888-8-4-4-40444222-2-2-20006i−6i0−2i62i600-1100−3i3i0000i6−i6i6−i6ζ5−2ζ7−ζ13+2ζ23−ζ5+2ζ7+ζ13−2ζ23−2ζ5+ζ7+2ζ13−ζ232ζ5−ζ7−2ζ13+ζ2300000000000000000000000000000000000000000000000
χ898-8-4-4-40444222-2-2-2000−6i6i02i6−2i600-11003i−3i0000−i6i6−i6i62ζ5−ζ7−2ζ13+ζ23−2ζ5+ζ7+2ζ13−ζ23−ζ5+2ζ7+ζ13−2ζ23ζ5−2ζ7−ζ13+2ζ2300000000000000000000000000000000000000000000000
χ908-8-4-4-40444222-2-2-2000−6i6i0−2i62i600-11003i−3i0000i6−i6i6−i6−2ζ5+ζ7+2ζ13−ζ232ζ5−ζ7−2ζ13+ζ23ζ5−2ζ7−ζ13+2ζ23−ζ5+2ζ7+ζ13−2ζ2300000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.