Finite Group Databasebeta

← Group #13167807

Character table — Group #13167807

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87
size11222222244444444444488888888888888888889912121212121218181818181818242424242424242424242424363636363636363636364848484848487272108108
order123334666333666812121224243612121212122424242424242424242424244422244422244121266666612121212121266688812122424666121212242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-111-11-1-1-1-111-11111-1-11111-1-11-11-1-1-1-111-111-111-1-1-1-1
χ3111111111111111111111111111111111111111111-1-11-1-111-1-1-1-1111-1-1-1-111-1-1-1-11-11-11-1-1-1-1111-1-11-1-1-1-111
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
χ51111111111111111111111111111111111111111-1-1111-1-11-11-11-1-1-11111111-1-1-1-11-1-11-11-11-1-1-11111-1-11-1-1-1
χ61111111111111111111111111111111111111111-1-111-1-1-1-1-1-11-11-1-1-11111-1-1-1-1-1-1-11-1-1-1-11-11-1-1-111-1-1-1-1111
χ71111111111111111111111111111111111111111-1-1-1-11111-1-11-11-1-11-1-1-1-111111111-1-1-1-11-11-1-11-1-1111-11-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-111-1-11-11-1-1-1-1-1-1-1-1-1-11111-1-1-11-11-11-1-1-1-1-1-1-1111-111
χ9111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1111111111-11-11-11-11-1-1111-1-1-111-1-111-1-11-1-1-1-11
χ10111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-111-1-1-1-111-11-11-1-111-11-11-11-1-111-1-1-1-1-11-111-1111-1
χ11111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-111-11-11-1-1-1-1111-11-111-1-11-11-1-11-1-111-1-1-1-11-11-1-1111-11
χ12111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1111111111-1-11-11-11-11-111111-1-1-111-1-1-1-111-11-1-11-1
χ13111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-11-11-1-1-111-11-11-1-11-11-1-1-111-111-11111-1-1-11-111-1
χ14111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-11-11-1-1-11-11-1-11-11-1111-1-111-1-1111-11-11-111-1-11
χ15111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-11-11-111-11-11-1-11-1-111-1-11111-11-11-11-11-1
χ16111111111111111-1111-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-11-1-1-1-1-11-11-111-11-11-1-111-111-111-1-1111-1-11-11
χ1722222-22222222220-2-2-20022-2-2-2-2-200000000000022000000-22-2-2222000000000000-2-22000-22000000000000
χ1822222-22222222220-2-2-20022-2-2-2-2-200000000000022000000-2-222-2220000000000002-2-20002-2000000000000
χ1922222-22222222220-2-2-20022-2-2-2-2-2000000000000-2-2000000222-2-2-2-2000000000000222000-2-2000000000000
χ2022222-22222222220-2-2-20022-2-2-2-2-2000000000000-2-20000002-2-222-2-2000000000000-22-200022000000000000
χ212222-12-1222-1-1-1-122-12222-1-1-1-12-1-12-122-1-1-1-1-1-1-1-1002220020202000222-1-1-1-10000200-1020-1000-1-1-1-100-1000
χ222222-12-1222-1-1-1-122-12222-1-1-1-12-1-12-122-1-1-1-1-1-1-1-10022-200-20-20-2000-222-1-1110000-20010-2010001-1-11001000
χ232222-12-1222-1-1-1-122-12222-1-1-1-12-1-12-122-1-1-1-1-1-1-1-100-2-220020-20-20002-2-211-1-1000020010-201000-111-1001000
χ242222-12-1222-1-1-1-122-12222-1-1-1-12-1-12-122-1-1-1-1-1-1-1-100-2-2-200-20202000-2-2-211110000-200-1020-1000111100-1000
χ252222-12-1222-1-1-1-12-2-122-2-2-1-1-1-12-1-1-21-2-211111111002-2200-2020200022-2-11-110000-200-10-20-1000-1-111001000
χ262222-12-1222-1-1-1-12-2-122-2-2-1-1-1-12-1-1-21-2-211111111002-2-20020-20-2000-22-2-111-10000200102010001-11-100-1000
χ272222-12-1222-1-1-1-12-2-122-2-2-1-1-1-12-1-1-21-2-21111111100-22200-20-20-20002-221-1-110000-20010201000-11-1100-1000
χ282222-12-1222-1-1-1-12-2-122-2-2-1-1-1-12-1-1-21-2-21111111100-22-20020202000-2-221-11-10000200-10-20-100011-1-1001000
χ29222-1222-12-12-1-12-122-12-1-1-1-1-12-1-1-122-1-122-1-1-1-1-1-12222022020000-1-10-1-12200-1-12200-1020000-1-10-1-10-1-10000
χ30222-1222-12-12-1-12-122-12-1-1-1-1-12-1-1-122-1-122-1-1-1-1-1-122-2-20-2-2020000-1-1011-2-20011-2-200-1020000-1-10110110000
χ31222-1222-12-12-1-12-122-12-1-1-1-1-12-1-1-122-1-122-1-1-1-1-1-1-2-2220-2-20-20000110-1-1220011-2-20010-20000110-1-10110000
χ32222-1222-12-12-1-12-122-12-1-1-1-1-12-1-1-122-1-122-1-1-1-1-1-1-2-2-2-20220-2000011011-2-200-1-1220010-20000110110-1-10000
χ33222-1222-12-12-1-12-1-22-1211-1-1-12-1-1-1-2-211-2-2111111222-202-2020000-1-10-112-200-112-200-10-20000110-110-110000
χ34222-1222-12-12-1-12-1-22-1211-1-1-12-1-1-1-2-211-2-211111122-220-22020000-1-101-1-22001-1-2200-10-200001101-101-10000
χ35222-1222-12-12-1-12-1-22-1211-1-1-12-1-1-1-2-211-2-2111111-2-22-20-220-20000110-112-2001-1-22001020000-1-10-1101-10000
χ36222-1222-12-12-1-12-1-22-1211-1-1-12-1-1-1-2-211-2-2111111-2-2-2202-20-200001101-1-2200-112-2001020000-1-101-10-110000
χ3722-122222-1-1-122-1-1222-122-1-12-1-1-1-1-12-1-1-1-122-1-1-1-1000022220020200-100002222-1-1-1-1000020-100-100-1-1-10-100
χ3822-122222-1-1-122-1-1222-122-1-12-1-1-1-1-12-1-1-1-122-1-1-1-100002-2-2200-20-200-1000022-2-211-110000-20100-100-1110100
χ3922-122222-1-1-122-1-1222-122-1-12-1-1-1-1-12-1-1-1-122-1-1-1-10000-222-200-20-20010000-2-222-1-1110000-201001001-1-10100
χ4022-122222-1-1-122-1-1222-122-1-12-1-1-1-1-12-1-1-1-122-1-1-1-10000-2-2-2-2002020010000-2-2-2-2111-1000020-1001001110-100
χ4122-122222-1-1-122-1-1-222-1-2-2-1-12-1-1-1-11-21111-2-21111000022-2-20020200-100002-22-2-111-10000-20-100-1001-110100
χ4222-122222-1-1-122-1-1-222-1-2-2-1-12-1-1-1-11-21111-2-2111100002-22-200-20-200-100002-2-221-111000020100-10011-10-100
χ4322-122222-1-1-122-1-1-222-1-2-2-1-12-1-1-1-11-21111-2-211110000-22-2200-20-20010000-222-2-11-11000020100100-1-110-100
χ4422-122222-1-1-122-1-1-222-1-2-2-1-12-1-1-1-11-21111-2-211110000-2-222002020010000-22-221-1-1-10000-20-100100-11-10100
χ454444-2-4-2444-2-2-2-2402-4-400-2-222-42200000000000000000000040-400000000000000000-200020000000000000
χ464444-2-4-2444-2-2-2-2402-4-400-2-222-422000000000000000000000-404000000000000000002000-20000000000000
χ47444-24-44-24-24-2-24-20-42-400-2-22-422200000000000044000000-40000-2-200000000000002000000000000000000
χ48444-24-44-24-24-2-24-20-42-400-2-22-4222000000000000-4-400000040000220000000000000-2000000000000000000
χ49444-2-24-2-24-2-211-2-24-2-24-2-2111-2-2114-2-2-2-2-21111110044000000000000-2-2-2-2000000000000000000110000000
χ50444-2-24-2-24-2-211-2-24-2-24-2-2111-2-2114-2-2-2-2-211111100-4-40000000000002222000000000000000000-1-10000000
χ51444-2-24-2-24-2-211-2-2-4-2-2422111-2-211-422222-1-1-1-1-1-1004-4000000000000-22-220000000000000000001-10000000
χ52444-2-24-2-24-2-211-2-2-4-2-2422111-2-211-422222-1-1-1-1-1-100-440000000000002-22-2000000000000000000-110000000
χ5344-244-444-2-2-244-2-20-4-4200-2-2-42222000000000000000000000040-400000000000000-20000002000000000000
χ5444-244-444-2-2-244-2-20-4-4200-2-2-422220000000000000000000000-404000000000000002000000-2000000000000
χ5544-24-24-24-2-21-2-21-24-24-24411-21-211-2-2-2-211-2-21111000040040000000-20000-2-20000-200000000001001000000
χ5644-24-24-24-2-21-2-21-24-24-24411-21-211-2-2-2-211-2-211110000-400-400000002000022000020000000000-100-1000000
χ5744-24-24-24-2-21-2-21-2-4-24-2-4-411-21-2112222-1-122-1-1-1-10000400-40000000-20000-22000020000000000100-1000000
χ5844-24-24-24-2-21-2-21-2-4-24-2-4-411-21-2112222-1-122-1-1-1-10000-40040000000200002-20000-20000000000-1001000000
χ5944-2-2444-2-21-2-2-2-2144-2-2-2-211-2-2111-2411-2-2-2-211110000044000000000000000-2-2-2-2000000000000000110000
χ6044-2-2444-2-21-2-2-2-2144-2-2-2-211-2-2111-2411-2-2-2-2111100000-4-40000000000000002222000000000000000-1-10000
χ6144-2-2444-2-21-2-2-2-21-44-2-22211-2-21112-4-1-12222-1-1-1-1000004-4000000000000000-22-220000000000000001-10000
χ6244-2-2444-2-21-2-2-2-21-44-2-22211-2-21112-4-1-12222-1-1-1-100000-440000000000000002-22-2000000000000000-110000
χ634-44440-4-4-4444-4-4-40000004-4000000000000000004i−4i000000000004i−4i00000000000000000000000000000000
χ644-44440-4-4-4444-4-4-40000004-400000000000000000−4i4i00000000000−4i4i00000000000000000000000000000000
χ654-44-240-42-4-24-22-420000i6−i6-220000000i6−i600i6−i6i6i6−i6−i64i−4i00000000000−2i2i000000000000000000006−60000000000
χ664-44-240-42-4-24-22-420000i6−i6-220000000i6−i600i6−i6i6i6−i6−i6−4i4i000000000002i−2i00000000000000000000−660000000000
χ674-44-240-42-4-24-22-420000−i6i6-220000000−i6i600−i6i6−i6−i6i6i64i−4i00000000000−2i2i00000000000000000000−660000000000
χ684-44-240-42-4-24-22-420000−i6i6-220000000−i6i600−i6i6−i6−i6i6i6−4i4i000000000002i−2i000000000000000000006−60000000000
χ69888-4-4-8-4-48-4-422-4-4044-80022-244-2-200000000000000000000000000000000000000000000000000000000000
χ7088-48-4-8-48-4-42-4-42-404-8400224-24-2-200000000000000000000000000000000000000000000000000000000000
χ7188-4-48-88-4-42-4-4-4-420-844002244-2-2-200000000000000000000000000000000000000000000000000000000000
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
χ768-888-404-8-88-4-444-8000000-440000000000000000000000000000000000000000000000000000000000000000
χ778-88-4-4044-8-4-42-24400002i6−2i62-200000002i6−2i600−i6i6−i6−i6i6i600000000000000000000000000000000000000000000000
χ788-88-4-4044-8-4-42-2440000−2i62i62-20000000−2i62i600i6−i6i6i6−i6−i600000000000000000000000000000000000000000000000
χ798-8-4880-8-84-4-48-844000000-440000000000000000000000000000000000000000000000000000000000000000
χ808-8-48-404-84-42-44-240000002-2000000000−3i23i200−3i23i23i2−3i200000000000000000000000000000000000000000000000
χ818-8-48-404-84-42-44-240000002-20000000003i2−3i2003i2−3i2−3i23i200000000000000000000000000000000000000000000000
χ828-8-4-480-8442-4-444-200002i6−2i62-20000000−i6i6002i6−2i6−i6−i6i6i600000000000000000000000000000000000000000000000
χ838-8-4-480-8442-4-444-20000−2i62i62-20000000i6−i600−2i62i6i6i6−i6−i600000000000000000000000000000000000000000000000
χ848-8-4-4-40444222-2-2-200002i6−2i6-1100033−3300−i6i6−3i23i2−i6i62ζ5+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−i6i63i2−3i2−i6i6−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−i63i2−3i2i6−i6−2ζ5−2ζ7−ζ13−ζ23ζ5+ζ7+2ζ13+2ζ232ζ5+2ζ7+ζ13+ζ23−ζ5−ζ7−2ζ13−2ζ2300000000000000000000000000000000000000000000000
χ878-8-4-4-40444222-2-2-20000−2i62i6-11000−333300i6−i6−3i23i2i6−i6ζ5+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.