Finite Group Databasebeta

← Group #13167811

Character table — Group #13167811

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1122222222244444444444444488888888888888888999999121212121212181818181818181818181818181818242424242424242424242424363636363636363636484848484848108108
order12333466688333666121212242424242424361212121212242424242424242424242244442244442246688888812121212666612121212121212126612242424242424661212121222
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
χ3111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-111
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-11111-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-1-1-1-1-11111-1-1
χ51111111111111111111111111111111111111111111-1-111-1-11111-1-11-1-1-1-1-1-111-1-111-1-1111111-1-111-1-11-1-1-1-111-1-11111-1-1-1-1
χ61111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-1111-1-1-1-111-1-1-1-1-1-11111
χ71111111111111111111111111111111111111111111-1-1-1-11111-1-111-11-1-1-1-1-1-1-111-1-1111111-1-111-1-111-11-1-1-1-1-11111-1-111-1-1
χ81111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-11-1-1-1-1-1-1-111-1-111-1-1-1-111-1-111-1-1-11-1-1-1-1-111-1-111-1-111
χ9111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-11111111-11-11-111111-1-1-1-1-1-1111111-1-11-11-11-11-1111-1-1-1-1-1-11-11-11-11-1
χ10111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-11-11-1111111-1-1-1-1-1-11111-1-111-11-11-11-11111-1-1-1-1-1-1-11-11-11-11
χ11111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-11-11-1-1111-1-11111-1-1-1-111-1-1-11-11-11-11-1-11-1-111111-1-11-111-1
χ12111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-11-1-1-1111-1-11111-1-1-1-1-1-1111-11-11-11-1-1-11-1-11111-111-11-1-11
χ13111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-1-111-1-1-1-111-1-11111-1-111-1-11-1-111-1-111-1-111-1-1111-11-1-11-11
χ14111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-111-11-1-1-1-111-1-11111-1-1-1-111-111-1-111-11-1-111-1-111-11-111-11-1
χ15111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111-1-11-1-1-11111-1-1-1-11111-1-1-111-1-111-1-11-11111-1-11-1-111-1-11
χ16111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11-11-1-1-11111-1-1-1-111-1-1111-1-111-1-11-11-11111-1-1-111-1-111-1
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
χ212222-122-12222-1-1-12-12-122222-1-1-1-1-12-1-1-122-1-1-1-1-1-1-1-10000222200220200000002200-1-12-12-100-1-100220-100000-1-1-1-100-1-100
χ222222-122-12222-1-1-12-12-122222-1-1-1-1-12-1-1-122-1-1-1-1-1-1-1-1000022-2-200-2-20200000002200-1-1-21-21001100-2-20-100000-1-111001100
χ232222-122-12222-1-1-12-12-122222-1-1-1-1-12-1-1-122-1-1-1-1-1-1-1-10000-2-22200-2-20-20000000-2-200112-12-1001100-2-2010000011-1-1001100
χ242222-122-12222-1-1-12-12-122222-1-1-1-1-12-1-1-122-1-1-1-1-1-1-1-10000-2-2-2-200220-20000000-2-20011-21-2100-1-100220100000111100-1-100
χ252222-122-12-2-22-1-1-12-12-12-2-2-2-211-1-1-12-1-1-1-2-2111111110000222-2002-2020000000-2-200-1-12-1-2100-11002-20-10000011-1100-1100
χ262222-122-12-2-22-1-1-12-12-12-2-2-2-211-1-1-12-1-1-1-2-211111111000022-2200-22020000000-2-200-1-1-212-1001-100-220-100000111-1001-100
χ272222-122-12-2-22-1-1-12-12-12-2-2-2-211-1-1-12-1-1-1-2-2111111110000-2-22-200-220-200000002200112-1-21001-100-220100000-1-1-11001-100
χ282222-122-12-2-22-1-1-12-12-12-2-2-2-211-1-1-12-1-1-1-2-2111111110000-2-2-22002-20-20000000220011-212-100-11002-20100000-1-11-100-1100
χ29222-122-12222-12-1-1-12-12222-1-122-1-1-1-12-1-1-1-122-1-1-1-1-1-100220022220020000002200-1-100-12-12-1-1002200-10000-1-100-1-1-1-10000
χ30222-122-12222-12-1-1-12-12222-1-122-1-1-1-12-1-1-1-122-1-1-1-1-1-1002200-2-2-2-20020000002200-1-1001-21-21100-2-200-10000-1-10011110000
χ31222-122-12222-12-1-1-12-12222-1-122-1-1-1-12-1-1-1-122-1-1-1-1-1-100-2-20022-2-200-2000000-2-2001100-12-121100-2-200100001100-1-1110000
χ32222-122-12222-12-1-1-12-12222-1-122-1-1-1-12-1-1-1-122-1-1-1-1-1-100-2-200-2-22200-2000000-2-20011001-21-2-1-100220010000110011-1-10000
χ33222-122-122-2-2-12-1-1-12-122-2-211-2-2-1-1-1-12-1-111-2-21111110022002-22-2002000000-2-200-1-100-121-2-11002-200-100001100-11-110000
χ34222-122-122-2-2-12-1-1-12-122-2-211-2-2-1-1-1-12-1-111-2-2111111002200-22-22002000000-2-200-1-1001-2-121-100-2200-1000011001-11-10000
χ35222-122-122-2-2-12-1-1-12-122-2-211-2-2-1-1-1-12-1-111-2-211111100-2-2002-2-2200-200000022001100-121-21-100-220010000-1-100-111-10000
χ36222-122-122-2-2-12-1-1-12-122-2-211-2-2-1-1-1-12-1-111-2-211111100-2-200-222-200-2000000220011001-2-12-11002-20010000-1-1001-1-110000
χ3722-122222-122-1-122-1-122-1-1-12222-1-12-1-1-1-1-1-1-1-122-1-1-1-1220000002222002-1-1220000000000002222-1-1-1-100-1-1-1000000-1-1-1-100
χ3822-122222-122-1-122-1-122-1-1-12222-1-12-1-1-1-1-1-1-1-122-1-1-1-122000000-2-2-2-2002-1-122000000000000-2-2-2-2111100-1-1-1000000111100
χ3922-122222-122-1-122-1-122-1-1-12222-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-200000022-2-200-211-2-200000000000022-2-2-1-11100111000000-1-11100
χ4022-122222-122-1-122-1-122-1-1-12222-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-2000000-2-22200-211-2-2000000000000-2-22211-1-10011100000011-1-100
χ4122-122222-1-2-2-1-122-1-122-111-2-2-2-2-1-12-1-1-1-11111-2-21111220000002-22-2002-1-1-2-20000000000002-22-2-11-1100-111000000-11-1100
χ4222-122222-1-2-2-1-122-1-122-111-2-2-2-2-1-12-1-1-1-11111-2-2111122000000-22-22002-1-1-2-2000000000000-22-221-11-100-1110000001-11-100
χ4322-122222-1-2-2-1-122-1-122-111-2-2-2-2-1-12-1-1-1-11111-2-21111-2-20000002-2-2200-211220000000000002-2-22-111-1001-1-1000000-111-100
χ4422-122222-1-2-2-1-122-1-122-111-2-2-2-2-1-12-1-1-1-11111-2-21111-2-2000000-222-200-21122000000000000-222-21-1-11001-1-10000001-1-1100
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
χ534444-2-44-24004-2-2-24-2-42-4000000-2-22-422200000000000000440000000-400000000000-2-200000000000002000000000000000
χ544444-2-44-24004-2-2-24-2-42-4000000-2-22-422200000000000000-4-40000000400000000000220000000000000-2000000000000000
χ55444-24-4-24400-24-2-2-242-4-4000000-2-222-4220000000000004400000000-40000000000-2-20000000000000020000000000000000
χ56444-24-4-24400-24-2-2-242-4-4000000-2-222-422000000000000-4-400000000400000000002200000000000000-20000000000000000
χ57444-2-24-2-2444-2-211-2-2-2-2444-2-2-2-2111-2-211-2-2-2-2111111000000440000000000000000000-2-2-2-20000000000000000011000000
χ58444-2-24-2-2444-2-211-2-2-2-2444-2-2-2-2111-2-211-2-2-2-2111111000000-4-40000000000000000000222200000000000000000-1-1000000
χ59444-2-24-2-24-4-4-2-211-2-2-2-24-4-42222111-2-2112222-1-1-1-1-1-10000004-40000000000000000000-2-222000000000000000001-1000000
χ60444-2-24-2-24-4-4-2-211-2-2-2-24-4-42222111-2-2112222-1-1-1-1-1-1000000-44000000000000000000022-2-200000000000000000-11000000
χ6144-244-444-200-2-244-2-2-4-42000000-2-2-42222000000000044000000000000-4-2-2000000000000000000000000200000000000000
χ6244-244-444-200-2-244-2-2-4-42000000-2-2-422220000000000-4-4000000000000422000000000000000000000000-200000000000000
χ6344-24-244-2-244-21-2-2-214-2-2-2-244-2-211-2-2111-2-211-2-21111000000000044000000000000000000000-2-200-2-200000000000001100
χ6444-24-244-2-244-21-2-2-214-2-2-2-244-2-211-2-2111-2-211-2-211110000000000-4-40000000000000000000002200220000000000000-1-100
χ6544-24-244-2-2-4-4-21-2-2-214-2-222-4-42211-2-211122-1-122-1-1-1-100000000004-4000000000000000000000-2200-2200000000000001-100
χ6644-24-244-2-2-4-4-21-2-2-214-2-222-4-42211-2-211122-1-122-1-1-1-10000000000-440000000000000000000002-2002-20000000000000-1100
χ6744-2-244-24-2441-2-2-21-2-24-2-2-2-2-24411-21-21111-2-2-2-211110000000044000000000000000000000-2-200-2-20000000000000110000
χ6844-2-244-24-2441-2-2-21-2-24-2-2-2-2-24411-21-21111-2-2-2-2111100000000-4-40000000000000000000002200220000000000000-1-10000
χ6944-2-244-24-2-4-41-2-2-21-2-24-22222-4-411-21-211-1-12222-1-1-1-1000000004-4000000000000000000000-2200-2200000000000001-10000
χ7044-2-244-24-2-4-41-2-2-21-2-24-22222-4-411-21-211-1-12222-1-1-1-100000000-440000000000000000000002-2002-20000000000000-110000
χ714-444-20-42-422−224-2-22-4200022−2222−22−22-220000022−22−22−22−2−22200004i−4i000000000000000−2i22i200−2i2i0000000000000000000i2−i200000000
χ724-444-20-42-422−224-2-22-4200022−2222−22−22-220000022−22−22−22−2−2220000−4i4i0000000000000002i2−2i2002i−2i0000000000000000000−i2i200000000
χ734-444-20-42-4−22224-2-22-42000−2222−22222−2-2200000−22222−22−222−2−200004i−4i0000000000000002i2−2i200−2i2i0000000000000000000−i2i200000000
χ744-444-20-42-4−22224-2-22-42000−2222−22222−2-2200000−22222−22−222−2−20000−4i4i000000000000000−2i22i2002i−2i0000000000000000000i2−i200000000
χ754-44-2402-4-422−22-24-222-400022−22−2222−22-2200000−2222−22−22−2−222004i−4i000000000000000−2i22i200−2i2i0000000000000000000i2−i20000000000
χ764-44-2402-4-422−22-24-222-400022−22−2222−22-2200000−2222−22−22−2−22200−4i4i0000000000000002i2−2i2002i−2i0000000000000000000−i2i20000000000
χ774-44-2402-4-4−2222-24-222-4000−22222−2−2222-22000002−2−22222−222−2−2004i−4i0000000000000002i2−2i200−2i2i0000000000000000000−i2i20000000000
χ784-44-2402-4-4−2222-24-222-4000−22222−2−2222-22000002−2−22222−222−2−200−4i4i000000000000000−2i22i2002i−2i0000000000000000000i2−i20000000000
χ794-4-2440-4-4222−22-2-24-422000−2222−2222−22-2200000−22−2222−22−2−2224-40000000000000-2222−2200000000000000000000000−22000000000000
χ804-4-2440-4-4222−22-2-24-422000−2222−2222−22-2200000−22−2222−22−2−222-4400000000000002-2−2222000000000000000000000002−2000000000000
χ814-4-2440-4-42−2222-2-24-4220002−2−2222−2222-22000002−22−2−222222−2−24-40000000000000-22−2222000000000000000000000002−2000000000000
χ824-4-2440-4-42−2222-2-24-4220002−2−2222−2222-22000002−22−2−222222−2−2-4400000000000002-222−2200000000000000000000000−22000000000000
χ83888-4-4-8-4-4800-4-422-4-444-800000022-244-2-2000000000000000000000000000000000000000000000000000000000000000000
χ8488-48-4-88-4-400-42-4-4-42-8440000002244-2-2-2000000000000000000000000000000000000000000000000000000000000000000
χ8588-4-48-8-48-4002-4-4-42-44-84000000224-24-2-2000000000000000000000000000000000000000000000000000000000000000000
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
χ908-88-4-4044-842−42-4-42-24400042−42−2222−22222-200000−2222−22222−222−2−200000000000000000000000000000000000000000000000000000000
χ918-88-4-4044-8−4242-4-42-244000−424222−2222−222-20000022−2222−22−22−2−22200000000000000000000000000000000000000000000000000000000
χ928-8-48-40-84442−42-42-444-2000−222242−42−22222-200000−22222−2−222222−2−200000000000000000000000000000000000000000000000000000000
χ938-8-48-40-844−4242-42-444-200022−22−424222−222-20000022−22−2222−22−2−22200000000000000000000000000000000000000000000000000000000
χ948-8-4-4804-8442−422-4-44-24000−2222−222242−422-2000002−2−2222−222222−2−200000000000000000000000000000000000000000000000000000000
χ958-8-4-4804-84−42422-4-44-2400022−2222−22−42422-200000−2222−2222−22−2−22200000000000000000000000000000000000000000000000000000000
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.