Finite Group Databasebeta

← Group #13167808

Character table — Group #13167808

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1122222222244444444444444488888888888888888999999121212121212181818181818181818181818181818242424242424242424242424363636363636363636484848484848108108
order12333466688333666121212242424242424361212121212242424242424242424242244442222442246688888812121212666666661212121266122424242424246666121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111-1-111-1-111-1-1111-1-1-1-1-1-111-1-111-1-111-1-111-1-111111-1-1-1-111-1-111-1-111-1-1
χ61111111111111111111111111111111111111111111-1-111-1-1-1-111-1-11-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1-1-11-1-1-1-111-1-1-1-111-1-111
χ71111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-1-111-1-11111-1-111-1-1-1-1-1-1-11-1-1-1-1-11111-1-1-1-111
χ81111111111111111111111111111111111111111111-1-1-1-111-1-11111-11-1-1-1-1-1-1-111-1-111-1-111-1-1111111-11-1-1-1-1-111-1-11111-1-1
χ9111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111111-11-11-111111-1-1-1-1-1-111111-11-11-11-111-1-1111-1-1-1-1-1-11-11-11-11-1
χ10111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-11-11-1111111-1-1-1-1-1-11111-11-11-11-11-1-111111-1-1-1-1-1-1-11-11-11-11
χ11111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-11-1-11-1-1111-1-11111-1-1-1-11-11-11-11-1-1-111-1-11-1-111111-11-1-11-11
χ12111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11-111-1-1-1111-1-11111-1-1-1-1-11-11-11-1111-1-1-1-11-1-11111-11-111-11-1
χ13111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-11-1-1-1-111-1-11111-1-11-1-111-1-1111-1-11-1-111-1-1111-1-111-1-11
χ14111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1-1-111-1-11111-1-1-111-1-111-1-1-1111-1-111-1-111-111-1-111-1
χ15111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-11-11-1-1-11111-1-1-1-1111-1-111-1-11-1-111-11-11111-1-11-1-11-111-1
χ16111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-11-1-11-1-1-11111-1-1-1-111-111-1-111-111-1-1-11-11111-1-1-111-11-1-11
χ1722222-222200222222-2-2-200000022-2-2-2-2-20000000000222222000000-2-2-2220000002222000000000000-2-2-200000000000000
χ1822222-222200222222-2-2-200000022-2-2-2-2-2000000000022-2-2-2-200000022-222000000-2-2-2-200000000000022-200000000000000
χ1922222-222200222222-2-2-200000022-2-2-2-2-20000000000-2-222-2-2000000-222-2-200000022-2-2000000000000-22200000000000000
χ2022222-222200222222-2-2-200000022-2-2-2-2-20000000000-2-2-2-2220000002-22-2-2000000-2-2220000000000002-2200000000000000
χ212222-12-122222-1-1-1-12-1222222-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-1220000222200002-1-122000000002222-1-1-1-1000000-1-1-10000-1-1-1-10000
χ222222-12-122222-1-1-1-12-1222222-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-1220000-2-2-2-200002-1-12200000000-2-2-2-21111000000-1-1-1000011110000
χ232222-12-122222-1-1-1-12-1222222-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-1-2-2000022-2-20000-211-2-20000000022-2-2-1-1110000001110000-1-1110000
χ242222-12-122222-1-1-1-12-1222222-1-1-1-1-1-12-1-122-1-1-1-1-1-1-1-1-2-20000-2-2220000-211-2-200000000-2-22211-1-1000000111000011-1-10000
χ252222-12-122-2-22-1-1-1-12-122-2-2-2-211-1-1-1-12-1-1-2-2111111112200002-22-200002-1-1-2-2000000002-22-2-11-11000000-1110000-11-110000
χ262222-12-122-2-22-1-1-1-12-122-2-2-2-211-1-1-1-12-1-1-2-211111111220000-22-2200002-1-1-2-200000000-22-221-11-1000000-11100001-11-10000
χ272222-12-122-2-22-1-1-1-12-122-2-2-2-211-1-1-1-12-1-1-2-211111111-2-200002-2-220000-21122000000002-2-22-111-10000001-1-10000-111-10000
χ282222-12-122-2-22-1-1-1-12-122-2-2-2-211-1-1-1-12-1-1-2-211111111-2-20000-222-20000-2112200000000-222-21-1-110000001-1-100001-1-110000
χ29222-12222-122-12-12-1-122-122-1-122-1-12-1-1-1-1-1-122-1-1-1-1-1-10000220022220200000002200-1-100-1-100222-12-10-100000-1-100-1-1-1-100
χ30222-12222-122-12-12-1-122-122-1-122-1-12-1-1-1-1-1-122-1-1-1-1-1-100002200-2-2-2-20200000002200-1-1001100-2-2-21-210-100000-1-100111100
χ31222-12222-122-12-12-1-122-122-1-122-1-12-1-1-1-1-1-122-1-1-1-1-1-10000-2-20022-2-20-20000000-2-2001100-1-10022-21-2101000001100-1-11100
χ32222-12222-122-12-12-1-122-122-1-122-1-12-1-1-1-1-1-122-1-1-1-1-1-10000-2-200-2-2220-20000000-2-20011001100-2-22-12-10100000110011-1-100
χ33222-12222-1-2-2-12-12-1-122-1-2-211-2-2-1-12-1-1-1-111-2-2111111000022002-22-2020000000-2-200-1-100-11002-22-1-210-1000001100-11-1100
χ34222-12222-1-2-2-12-12-1-122-1-2-211-2-2-1-12-1-1-1-111-2-211111100002200-22-22020000000-2-200-1-1001-100-22-212-10-10000011001-11-100
χ35222-12222-1-2-2-12-12-1-122-1-2-211-2-2-1-12-1-1-1-111-2-21111110000-2-2002-2-220-2000000022001100-11002-2-212-10100000-1-100-111-100
χ36222-12222-1-2-2-12-12-1-122-1-2-211-2-2-1-12-1-1-1-111-2-21111110000-2-200-222-20-20000000220011001-100-222-1-210100000-1-1001-1-1100
χ3722-12222-1222-1-12-12-12-12-1-12222-1-1-12-1-1-1-1-1-1-122-1-1-1-100220022002220000002200-1-100-1-1002200-12-12-10000-1-100-1-100-1-100
χ3822-12222-1222-1-12-12-12-12-1-12222-1-1-12-1-1-1-1-1-1-122-1-1-1-1002200-2-200-2-220000002200-1-1001100-2-2001-21-2-10000-1-10011001100
χ3922-12222-1222-1-12-12-12-12-1-12222-1-1-12-1-1-1-1-1-1-122-1-1-1-100-2-2002200-2-2-2000000-2-2001100-1-10022001-21-2100001100-1-1001100
χ4022-12222-1222-1-12-12-12-12-1-12222-1-1-12-1-1-1-1-1-1-122-1-1-1-100-2-200-2-20022-2000000-2-20011001100-2-200-12-121000011001100-1-100
χ4122-12222-12-2-2-1-12-12-12-1211-2-2-2-2-1-1-12-1-1-11111-2-211110022002-2002-22000000-2-200-1-100-11002-200-121-2-100001100-1100-1100
χ4222-12222-12-2-2-1-12-12-12-1211-2-2-2-2-1-1-12-1-1-11111-2-21111002200-2200-222000000-2-200-1-1001-100-22001-2-12-1000011001-1001-100
χ4322-12222-12-2-2-1-12-12-12-1211-2-2-2-2-1-1-12-1-1-11111-2-2111100-2-2002-200-22-200000022001100-11002-2001-2-1210000-1-100-11001-100
χ4422-12222-12-2-2-1-12-12-12-1211-2-2-2-2-1-1-12-1-1-11111-2-2111100-2-200-22002-2-2000000220011001-100-2200-121-210000-1-1001-100-1100
χ452-22220-2-2-22−2222-2-2-20002−22−22−22-2000002−22−22−222−2−22-22i−2i2i−2i0000000002-22−2−i2i2−i2i22i−2i2i−2i0000000000000002−2−i2i2−i2i200000000
χ462-22220-2-2-22−2222-2-2-20002−22−22−22-2000002−22−22−222−2−22-2−2i2i−2i2i0000000002-22−2i2−i2i2−i2−2i2i−2i2i0000000000000002−2i2−i2i2−i200000000
χ472-22220-2-2-22−2222-2-2-20002−22−22−22-2000002−22−22−222−2−2-222i−2i−2i2i000000000-22−22−i2i2i2−i22i−2i−2i2i000000000000000−22−i2i2i2−i200000000
χ482-22220-2-2-22−2222-2-2-20002−22−22−22-2000002−22−22−222−2−2-22−2i2i2i−2i000000000-22−22i2−i2−i2i2−2i2i2i−2i000000000000000−22i2−i2−i2i200000000
χ492-22220-2-2-2−22222-2-2-2000−22−22−222-200000−22−22−22−2−2222-22i−2i2i−2i0000000002-2−22i2−i2i2−i22i−2i2i−2i000000000000000−22i2−i2i2−i200000000
χ502-22220-2-2-2−22222-2-2-2000−22−22−222-200000−22−22−22−2−2222-2−2i2i−2i2i0000000002-2−22−i2i2−i2i2−2i2i−2i2i000000000000000−22−i2i2−i2i200000000
χ512-22220-2-2-2−22222-2-2-2000−22−22−222-200000−22−22−22−2−222-222i−2i−2i2i000000000-222−2i2−i2−i2i22i−2i−2i2i0000000000000002−2i2−i2−i2i200000000
χ522-22220-2-2-2−22222-2-2-2000−22−22−222-200000−22−22−22−2−222-22−2i2i2i−2i000000000-222−2−i2i2i2−i2−2i2i2i−2i0000000000000002−2−i2i2i2−i200000000
χ534444-2-4-244004-2-2-2-242-4-4000000-2-222-422000000000044000000000000-4-2-2000000000000000000000000200000000000000
χ544444-2-4-244004-2-2-2-242-4-4000000-2-222-4220000000000-4-4000000000000422000000000000000000000000-200000000000000
χ55444-24-444-200-24-24-2-2-4-42000000-2-2-4222200000000000000440000000-400000000000-2-200000000000002000000000000000
χ56444-24-444-200-24-24-2-2-4-42000000-2-2-4222200000000000000-4-40000000400000000000220000000000000-2000000000000000
χ57444-2-24-24-244-2-21-21-2-24-244-2-2-2-211-21-211-2-2-2-211111100000000440000000000000000000-2-200-2-2000000000000000110000
χ58444-2-24-24-244-2-21-21-2-24-244-2-2-2-211-21-211-2-2-2-211111100000000-4-40000000000000000000220022000000000000000-1-10000
χ59444-2-24-24-2-4-4-2-21-21-2-24-2-4-4222211-21-2112222-1-1-1-1-1-1000000004-40000000000000000000-2200-220000000000000001-10000
χ60444-2-24-24-2-4-4-2-21-21-2-24-2-4-4222211-21-2112222-1-1-1-1-1-100000000-4400000000000000000002-2002-2000000000000000-110000
χ6144-244-44-2400-2-24-24-2-42-4000000-2-22-42220000000000004400000000-40000000000-2-20000000000000020000000000000000
χ6244-244-44-2400-2-24-24-2-42-4000000-2-22-4222000000000000-4-400000000400000000002200000000000000-20000000000000000
χ6344-24-24-2-2444-21-21-2-2-2-24-2-244-2-2111-2-211-2-211-2-21111000000440000000000000000000-2-200-2-200000000000000011000000
χ6444-24-24-2-2444-21-21-2-2-2-24-2-244-2-2111-2-211-2-211-2-21111000000-4-40000000000000000000220022000000000000000-1-1000000
χ6544-24-24-2-24-4-4-21-21-2-2-2-2422-4-422111-2-21122-1-122-1-1-1-10000004-40000000000000000000-2200-220000000000000001-1000000
χ6644-24-24-2-24-4-4-21-21-2-2-2-2422-4-422111-2-21122-1-122-1-1-1-1000000-4400000000000000000002-2002-2000000000000000-11000000
χ6744-2-2444-2-2441-2-2-2-214-2-2-2-2-2-24411-2-211111-2-2-2-2111100000000004400000000000000000000000-2-2-2-200000000000001100
χ6844-2-2444-2-2441-2-2-2-214-2-2-2-2-2-24411-2-211111-2-2-2-211110000000000-4-40000000000000000000000022220000000000000-1-100
χ6944-2-2444-2-2-4-41-2-2-2-214-2-22222-4-411-2-2111-1-12222-1-1-1-100000000004-400000000000000000000000-2-22200000000000001-100
χ7044-2-2444-2-2-4-41-2-2-2-214-2-22222-4-411-2-2111-1-12222-1-1-1-10000000000-440000000000000000000000022-2-20000000000000-1100
χ714-444-202-4-422−224-2-222-400022−2222−22−22-220000022−22−22−22−2−2224-40000000000000-2222−2200000000000000000000000−22000000000000
χ724-444-202-4-422−224-2-222-400022−2222−22−22-220000022−22−22−22−2−222-4400000000000002-2−2222000000000000000000000002−2000000000000
χ734-444-202-4-4−22224-2-222-4000−2222−22222−2-2200000−22222−22−222−2−24-40000000000000-22−2222000000000000000000000002−2000000000000
χ744-444-202-4-4−22224-2-222-4000−2222−22222−2-2200000−22222−22−222−2−2-4400000000000002-222−2200000000000000000000000−22000000000000
χ754-44-240-4-4222−22-24-2-42200022−22−2222−22-2200000−2222−22−22−2−22200004i−4i000000000000000−2i22i200−2i2i0000000000000000000i2−i200000000
χ764-44-240-4-4222−22-24-2-42200022−22−2222−22-2200000−2222−22−22−2−2220000−4i4i0000000000000002i2−2i2002i−2i0000000000000000000−i2i200000000
χ774-44-240-4-42−2222-24-2-422000−22222−2−2222-22000002−2−22222−222−2−200004i−4i0000000000000002i2−2i200−2i2i0000000000000000000−i2i200000000
χ784-44-240-4-42−2222-24-2-422000−22222−2−2222-22000002−2−22222−222−2−20000−4i4i000000000000000−2i22i2002i−2i0000000000000000000i2−i200000000
χ794-4-2440-42-422−22-2-242-42000−2222−2222−22-2200000−22−2222−22−2−222004i−4i000000000000000−2i22i200−2i2i0000000000000000000i2−i20000000000
χ804-4-2440-42-422−22-2-242-42000−2222−2222−22-2200000−22−2222−22−2−22200−4i4i0000000000000002i2−2i2002i−2i0000000000000000000−i2i20000000000
χ814-4-2440-42-4−2222-2-242-420002−2−2222−2222-22000002−22−2−222222−2−2004i−4i0000000000000002i2−2i200−2i2i0000000000000000000−i2i20000000000
χ824-4-2440-42-4−2222-2-242-420002−2−2222−2222-22000002−22−2−222222−2−200−4i4i000000000000000−2i22i2002i−2i0000000000000000000i2−i20000000000
χ83888-4-4-8-48-400-4-42-42-44-84000000224-24-2-2000000000000000000000000000000000000000000000000000000000000000000
χ8488-48-4-8-4-4800-42-42-4-444-800000022-244-2-2000000000000000000000000000000000000000000000000000000000000000000
χ8588-4-48-88-4-4002-4-4-4-42-8440000002244-2-2-2000000000000000000000000000000000000000000000000000000000000000000
χ8688-4-4-48-4-4-488222222-4-4-4-4-4-4-4-4-4-1-1222-1-1222222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ8788-4-4-48-4-4-4-8-8222222-4-4-4444444-1-1222-1-1-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ8888-4-4-4-8-4-4-400222222444000000-1-1-2-2-21100000033−3333−3300000000000000000000000000000000000000000000000000000000
χ8988-4-4-4-8-4-4-400222222444000000-1-1-2-2-211000000−3333−333300000000000000000000000000000000000000000000000000000000
χ908-88-4-404-8442−42-4-424-2400042−42−2222−22222-200000−2222−22222−222−2−200000000000000000000000000000000000000000000000000000000
χ918-88-4-404-84−4242-4-424-24000−424222−2222−222-20000022−2222−22−22−2−22200000000000000000000000000000000000000000000000000000000
χ928-8-48-4044-842−42-42-4-244000−222242−42−22222-200000−22222−2−222222−2−200000000000000000000000000000000000000000000000000000000
χ938-8-48-4044-8−4242-42-4-24400022−22−424222−222-20000022−22−2222−22−2−22200000000000000000000000000000000000000000000000000000000
χ948-8-4-480-84442−422-4-444-2000−2222−222242−422-2000002−2−2222−222222−2−200000000000000000000000000000000000000000000000000000000
χ958-8-4-480-844−42422-4-444-200022−2222−22−42422-200000−2222−2222−22−2−22200000000000000000000000000000000000000000000000000000000
χ968-8-4-4-4044442−42222-2-2-2000−2222−2222−2222-1100033−332−22−22−22ζ5−2ζ7−ζ13+ζ23−ζ5+ζ7+2ζ13−2ζ23−2ζ5+2ζ7+ζ13−ζ23ζ5−ζ7−2ζ13+2ζ2300000000000000000000000000000000000000000000000000000000
χ978-8-4-4-4044442−42222-2-2-2000−2222−2222−2222-11000−33332−22−22−2−ζ5+ζ7+2ζ13−2ζ232ζ5−2ζ7−ζ13+ζ23ζ5−ζ7−2ζ13+2ζ23−2ζ5+2ζ7+ζ13−ζ2300000000000000000000000000000000000000000000000000000000
χ988-8-4-4-40444−4242222-2-2-200022−2222−2222−22-1100033−33−22−22−22−2ζ5+2ζ7+ζ13−ζ23ζ5−ζ7−2ζ13+2ζ232ζ5−2ζ7−ζ13+ζ23−ζ5+ζ7+2ζ13−2ζ2300000000000000000000000000000000000000000000000000000000
χ998-8-4-4-40444−4242222-2-2-200022−2222−2222−22-11000−3333−22−22−22ζ5−ζ7−2ζ13+2ζ23−2ζ5+2ζ7+ζ13−ζ23−ζ5+ζ7+2ζ13−2ζ232ζ5−2ζ7−ζ13+ζ2300000000000000000000000000000000000000000000000000000000

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