Finite Group Databasebeta

← Group #13167810

Character table — Group #13167810

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222222244444444444488888888888888888889912121212121218181818181818242424242424242424242424363636363636363636364848484848487272108108
order12333466633366681212122424361212121212242424242424242424242424222444442244466661212121212121212121266888121212242461212121212242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-11-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1-1-111
χ3111111111111111111111111111111111111111111-1-11111-1-11-1-111-1-1-1-111111111-1-11-1-1-1-1111-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-111-1-1
χ51111111111111111111111111111111111111111-1-11111-1-11-1-11-1-1-1111111-1-111-1-11-1-11-11-1-1-1-11111-1-11-1-1-1
χ61111111111111111111111111111111111111111-1-111-1-111-11-1-11-1-11111-1-111-1-111-11-1-11-11-1-1-111-1-111-11-1-1
χ71111111111111111111111111111111111111111-1-1-1-111-1-1-11-1-11-1-1-1-1-1-111-1-111-1-1-11-1-11-11-1-1-1-1-111-1-1-1111
χ81111111111111111111111111111111111111111-1-1-1-1-1-1111-1-11-1-1-1-1-1-1-1-1-111-1-1111-1-11-11-1-1-1-1-1-1-1-1111-111
χ9111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111-11-11-1111111111-1-11-11-11-11-111-1-1-1111-1-11-11-11-1-1-11-1
χ10111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-11-1-11-1-11111-1-1-11-11-11-11-1-1-111-1-11-1-11-1-11-11111-1
χ11111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-111-11-1-1-11-1-111-1-1111-11-11-11-1-1-1-111-1-11-1-1-111-11-111-11
χ12111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-11-11-111111111-1-111-11-11-11-1111-1-1-1111-1-1-11-11-11-1-1-11
χ13111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-11-1-1-111-1-11-1-111-1-111-11-111-1-1111-11-1-11-11-11
χ14111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-11-1-11-1-111-1-1-111-1-111-1-1111-1-11-1111-1-111-11-1-11
χ15111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-1-11-1-1-1-1111-1-111-1-11-1111-1-11-111-111-1-111-11-1
χ16111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-11-1-11-1-1-1-1-111-111-1-111-11-11-111-1-111-11-111-1-111-1
χ1722222-22222222220-2-2-20022-2-2-2-2-20000000000002200000022-2-2-22200000000000022000-2-2-2000000000000
χ1822222-22222222220-2-2-20022-2-2-2-2-200000000000022000000-2-2-22222000000000000-2-200022-2000000000000
χ1922222-22222222220-2-2-20022-2-2-2-2-2000000000000-2-20000002-22-22-2-20000000000002-2000-222000000000000
χ2022222-22222222220-2-2-20022-2-2-2-2-2000000000000-2-2000000-2222-2-2-2000000000000-220002-22000000000000
χ212222-122-122-1-1-12-122-1222-1-1-12-1-1-12-122-1-1-1-1-1-1-1-10022002202002002-12-100-1-100220-10020-1000-1-100-1-10-100
χ222222-122-122-1-1-12-122-1222-1-1-12-1-1-12-122-1-1-1-1-1-1-1-1002200-2-20-200-2002-12-1001100-2-20100-201000-1-100110100
χ232222-122-122-1-1-12-122-1222-1-1-12-1-1-12-122-1-1-1-1-1-1-1-100-2-200220-200-200-21-2100-1-100220100-2010001100-1-10100
χ242222-122-122-1-1-12-122-1222-1-1-12-1-1-12-122-1-1-1-1-1-1-1-100-2-200-2-20200200-21-21001100-2-20-10020-10001100110-100
χ252222-122-122-1-1-12-1-22-12-2-2-1-1-12-1-1-1-21-2-211111111002-2002-202002002-1-2100-11002-20-100-20-1000-1100-110100
χ262222-122-122-1-1-12-1-22-12-2-2-1-1-12-1-1-1-21-2-211111111002-200-220-200-2002-1-21001-100-220100201000-11001-10-100
χ272222-122-122-1-1-12-1-22-12-2-2-1-1-12-1-1-1-21-2-21111111100-22002-20-200-200-212-100-11002-201002010001-100-110-100
χ282222-122-122-1-1-12-1-22-12-2-2-1-1-12-1-1-1-21-2-21111111100-2200-220200200-212-1001-100-220-100-20-10001-1001-10100
χ29222-122-122-12-1-1-122-12222-1-1-1-12-1-1-12-1-122-1-1-1-1-1-1002222002002000-12-12-1-1002200-10020-10000-1-1-1-100-1000
χ30222-122-122-12-1-1-122-12222-1-1-1-12-1-1-12-1-122-1-1-1-1-1-10022-2-200-200-2000-12-121100-2-200100-2010000-1-111001000
χ31222-122-122-12-1-1-122-12222-1-1-1-12-1-1-12-1-122-1-1-1-1-1-100-2-22200-200-20001-21-2-1-1002200100-201000011-1-1001000
χ32222-122-122-12-1-1-122-12222-1-1-1-12-1-1-12-1-122-1-1-1-1-1-100-2-2-2-20020020001-21-21100-2-200-10020-10000111100-1000
χ33222-122-122-12-1-1-12-2-122-2-2-1-1-1-12-1-11-211-2-2111111002-22-2002002000-121-2-11002-200-100-20-10000-11-11001000
χ34222-122-122-12-1-1-12-2-122-2-2-1-1-1-12-1-11-211-2-2111111002-2-2200-200-2000-121-21-100-22001002010000-111-100-1000
χ35222-122-122-12-1-1-12-2-122-2-2-1-1-1-12-1-11-211-2-211111100-222-200-200-20001-2-12-11002-20010020100001-1-1100-1000
χ36222-122-122-12-1-1-12-2-122-2-2-1-1-1-12-1-11-211-2-211111100-22-220020020001-2-121-100-2200-100-20-100001-11-1001000
χ3722-122222-1-1-122-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-12200222200200-1-100002222-1-1-1-10020000-1-1-100-1-1-1-10000
χ3822-122222-1-1-122-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-12200-2-2-2-200200-1-10000-2-2-2-211110020000-1-1-10011110000
χ3922-122222-1-1-122-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1-2-20022-2-200-20011000022-2-2-1-11100-2000011100-1-1110000
χ4022-122222-1-1-122-1-1222-1-1-1-1-12-1-1-1-122-1-1-1-122-1-1-1-1-2-200-2-22200-200110000-2-22211-1-100-200001110011-1-10000
χ4122-122222-1-1-122-1-1-222-111-1-12-1-1-1-1-2-21111-2-2111122002-22-200200-1-100002-22-2-11-1100-20000-11100-11-110000
χ4222-122222-1-1-122-1-1-222-111-1-12-1-1-1-1-2-21111-2-211112200-22-2200200-1-10000-22-221-11-100-20000-111001-11-10000
χ4322-122222-1-1-122-1-1-222-111-1-12-1-1-1-1-2-21111-2-21111-2-2002-2-2200-2001100002-2-22-111-100200001-1-100-111-10000
χ4422-122222-1-1-122-1-1-222-111-1-12-1-1-1-1-2-21111-2-21111-2-200-222-200-200110000-222-21-1-1100200001-1-1001-1-110000
χ454444-2-44-244-2-2-24-20-42-400-2-22-4222000000000000000000000400-4000000000000000-2000020000000000000
χ464444-2-44-244-2-2-24-20-42-400-2-22-4222000000000000000000000-400400000000000000020000-20000000000000
χ47444-24-4-244-24-2-2-2402-4-400-2-222-42200000000000000000000400-4000000000000000-20000200000000000000
χ48444-24-4-244-24-2-2-2402-4-400-2-222-42200000000000000000000-400400000000000000020000-200000000000000
χ49444-2-24-2-24-2-211-2-24-2-2444111-2-211-2-2-2-2-2-2111111004400000000000-2-2-2-20000000000000000001100000000
χ50444-2-24-2-24-2-211-2-24-2-2444111-2-211-2-2-2-2-2-211111100-4-4000000000002222000000000000000000-1-100000000
χ51444-2-24-2-24-2-211-2-2-4-2-24-4-4111-2-211222222-1-1-1-1-1-1004-400000000000-2-2220000000000000000001-100000000
χ52444-2-24-2-24-2-211-2-2-4-2-24-4-4111-2-211222222-1-1-1-1-1-100-440000000000022-2-2000000000000000000-1100000000
χ5344-244-444-2-2-244-2-20-4-4200-2-2-422220000000000004400000000-400-2-200000000000000000002000000000000
χ5444-244-444-2-2-244-2-20-4-4200-2-2-42222000000000000-4-400000000400220000000000000000000-2000000000000
χ5544-24-244-2-2-21-2-2-2144-2-2-2-211-2-21114-2-2-211-2-21111000000440000000000000-2-200-2-200000000000000110000
χ5644-24-244-2-2-21-2-2-2144-2-2-2-211-2-21114-2-2-211-2-21111000000-4-4000000000000022002200000000000000-1-10000
χ5744-24-244-2-2-21-2-2-21-44-2-22211-2-2111-4222-1-122-1-1-1-10000004-40000000000000-2200-22000000000000001-10000
χ5844-24-244-2-2-21-2-2-21-44-2-22211-2-2111-4222-1-122-1-1-1-1000000-4400000000000002-2002-200000000000000-110000
χ5944-2-244-24-21-2-2-21-24-24-2-2-211-21-211-2411-2-2-2-211110000440000000000000-2-200-2-20000000000000011000000
χ6044-2-244-24-21-2-2-21-24-24-2-2-211-21-211-2411-2-2-2-211110000-4-4000000000000022002200000000000000-1-1000000
χ6144-2-244-24-21-2-2-21-2-4-24-22211-21-2112-4-1-12222-1-1-1-100004-40000000000000-2200-22000000000000001-1000000
χ6244-2-244-24-21-2-2-21-2-4-24-22211-21-2112-4-1-12222-1-1-1-10000-4400000000000002-2002-200000000000000-11000000
χ634-44440-4-4-4444-4-4-40000004-4000000000000000004-4000000000004-400000000000000000000000000000000
χ644-44440-4-4-4444-4-4-40000004-400000000000000000-4400000000000-4400000000000000000000000000000000
χ654-4-2440-4-42-2-24-4220000i6−i6-220000000i6−i6i6−i600i6i6−i6−i64-400000000000-2200000000000000000000i6−i60000000000
χ664-4-2440-4-42-2-24-4220000i6−i6-220000000i6−i6i6−i600i6i6−i6−i6-44000000000002-200000000000000000000−i6i60000000000
χ674-4-2440-4-42-2-24-4220000−i6i6-220000000−i6i6−i6i600−i6−i6i6i64-400000000000-2200000000000000000000−i6i60000000000
χ684-4-2440-4-42-2-24-4220000−i6i6-220000000−i6i6−i6i600−i6−i6i6i6-44000000000002-200000000000000000000i6−i60000000000
χ69888-4-4-8-4-48-4-422-4-4044-80022-244-2-200000000000000000000000000000000000000000000000000000000000
χ7088-48-4-88-4-4-42-4-4-420-844002244-2-2-200000000000000000000000000000000000000000000000000000000000
χ7188-4-48-8-48-42-4-4-42-404-8400224-24-2-200000000000000000000000000000000000000000000000000000000000
χ7288-4-4-48-4-4-42222228-4-4-4-4-4-1-1222-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000
χ7388-4-4-48-4-4-4222222-8-4-4-444-1-1222-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000
χ7488-4-4-4-8-4-4-4222222044400-1-1-2-2-2110000000033−3333−3300000000000000000000000000000000000000000000000
χ7588-4-4-4-8-4-4-4222222044400-1-1-2-2-21100000000−3333−333300000000000000000000000000000000000000000000000
χ768-888-40-84-88-4-44-84000000-440000000000000000000000000000000000000000000000000000000000000000
χ778-88-4804-8-8-48-444-8000000-440000000000000000000000000000000000000000000000000000000000000000
χ788-88-4-4044-8-4-42-2440000002-200000000000−3i23i2−3i23i23i2−3i200000000000000000000000000000000000000000000000
χ798-88-4-4044-8-4-42-2440000002-2000000000003i2−3i23i2−3i2−3i23i200000000000000000000000000000000000000000000000
χ808-8-48-40-844-42-444-200002i6−2i62-200000002i6−2i6−i6i600−i6−i6i6i600000000000000000000000000000000000000000000000
χ818-8-48-40-844-42-444-20000−2i62i62-20000000−2i62i6i6−i600i6i6−i6−i600000000000000000000000000000000000000000000000
χ828-8-4-4804-842-4-44-2400002i6−2i62-20000000−i6i62i6−2i600−i6−i6i6i600000000000000000000000000000000000000000000000
χ838-8-4-4804-842-4-44-240000−2i62i62-20000000i6−i6−2i62i600i6i6−i6−i600000000000000000000000000000000000000000000000
χ848-8-4-4-40444222-2-2-200002i6−2i6-1100033−3300−i6i6−i6i6−3i23i22ζ5+2ζ7+ζ13+ζ23−ζ5−ζ7−2ζ13−2ζ23−2ζ5−2ζ7−ζ13−ζ23ζ5+ζ7+2ζ13+2ζ2300000000000000000000000000000000000000000000000
χ858-8-4-4-40444222-2-2-200002i6−2i6-11000−333300−i6i6−i6i63i2−3i2−ζ5−ζ7−2ζ13−2ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−2ζ5−2ζ7−ζ13−ζ2300000000000000000000000000000000000000000000000
χ868-8-4-4-40444222-2-2-20000−2i62i6-1100033−3300i6−i6i6−i63i2−3i2−2ζ5−2ζ7−ζ13−ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−ζ5−ζ7−2ζ13−2ζ2300000000000000000000000000000000000000000000000
χ878-8-4-4-40444222-2-2-20000−2i62i6-11000−333300i6−i6i6−i6−3i23i2ζ5+ζ7+2ζ13+2ζ23−2ζ5−2ζ7−ζ13−ζ23−ζ5−ζ7−2ζ13−2ζ232ζ5+2ζ7+ζ13+ζ2300000000000000000000000000000000000000000000000

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