Finite Group Databasebeta

← Group #13167804

Character table — Group #13167804

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1122222222244444444444444488888888888888888999999121212121212181818181818181818181818181818242424242424242424242424363636363636363636484848484848108108
order12333466688333666121212242424242424361212121212242424242424242424242244442224442246688888812121212666666121212121212661224242424242466612121224
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
χ3111111111111111111111111111111111111111111111-1-1-1-111-111-1-1-111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1111-1-1-1-111-111-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1111-1-1-1-1-1-11-1-1111
χ51111111111111111111111111111111111111111111-1-111-1-11-111-111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1111-1-1-1-111-1-11-111-11-1-1
χ61111111111111111111111111111111111111111111-1-111-1-1-11-1-11-11-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-111-1-11-1-1-1-111-1-1-11-1-11-111
χ71111111111111111111111111111111111111111111-1-1-1-1111-1-11-1-1-11-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-1-11-1-1-1-1-1111-1-11-1-111
χ81111111111111111111111111111111111111111111-1-1-1-111-111-111-11-1-1-1-1-1-1-111-1-111-1-11111-1-11111-11-1-1-1-1-111-111-111-1-1
χ9111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1111111-1-1-1-1-1-111111111-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-11-11
χ10111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1111-111111-1-1-1-1-1-11111-1-1-1-1111111-1-1111-1-1-1-1-1-1-1-1111-11-1
χ11111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111-1-1-1-1-1111-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-11111111-1-1-11-1
χ12111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11111-1-1-1111-11
χ13111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1111-1-1-1-111-1-11111-1-111-1-1-1-1-1-111111-1-111-1-1111-1-1-1111-1
χ14111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-11-1-1-1-111-1-11111-1-1-1-1111111-1-1-1-11-1-111-1-111-1111-1-1-11
χ15111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-11-1-11-1-1-11111-1-1-1-11111-1-111-1-111-1-1-11-11111-1-11-11-11-1-11
χ16111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-11-11-11-1-1-11111-1-1-1-111-1-111-1-111-1-111-11-11111-1-1-11-11-111-1
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
χ212222-1222-1222-1-12-1-122-12222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-10000220220220200000002200-1-1002-12-1002-12-10-100000-1-10-1-10-1-100
χ222222-1222-1222-1-12-1-122-12222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-10000220-2-20-2-20200000002200-1-100-21-2100-21-210-100000-1-101101100
χ232222-1222-1222-1-12-1-122-12222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-10000-2-202-202-20-20000000-2-20011002-1-21002-1-210100000110-110-1100
χ242222-1222-1222-1-12-1-122-12222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-10000-2-20-220-220-20000000-2-2001100-212-100-212-101000001101-101-100
χ252222-1222-1-2-22-1-12-1-122-1-2-2-2-211-1-12-1-1-1-1-2-21111111100002202-20-22020000000-2-200-1-1002-1-2100-212-10-100000110-1101-100
χ262222-1222-1-2-22-1-12-1-122-1-2-2-2-211-1-12-1-1-1-1-2-2111111110000220-2202-2020000000-2-200-1-100-212-1002-1-210-1000001101-10-1100
χ272222-1222-1-2-22-1-12-1-122-1-2-2-2-211-1-12-1-1-1-1-2-2111111110000-2-20220-2-20-20000000220011002-12-100-21-210100000-1-10-1-101100
χ282222-1222-1-2-22-1-12-1-122-1-2-2-2-211-1-12-1-1-1-1-2-2111111110000-2-20-2-20220-2000000022001100-21-21002-12-10100000-1-10110-1-100
χ29222-1222-1222-12-1-12-12-1222-1-122-1-1-12-1-1-1-1-122-1-1-1-1-1-100220020220220000002200-1-1002-100-122-100-12-10000-1-100-10-1-10-100
χ30222-1222-1222-12-1-12-12-1222-1-122-1-1-12-1-1-1-1-122-1-1-1-1-1-1002200-20-2-20-220000002200-1-100-21001-2-21001-2-10000-1-10010110100
χ31222-1222-1222-12-1-12-12-1222-1-122-1-1-12-1-1-1-1-122-1-1-1-1-1-100-2-20020-220-2-2000000-2-20011002-1001-22-1001-2100001100-101-10100
χ32222-1222-1222-12-1-12-12-1222-1-122-1-1-12-1-1-1-1-122-1-1-1-1-1-100-2-200-202-202-2000000-2-2001100-2100-12-2100-1210000110010-110-100
χ33222-1222-12-2-2-12-1-12-12-12-2-211-2-2-1-1-12-1-1-111-2-211111100220020-2-2022000000-2-200-1-1002-1001-2-2100-12-100001100-10110-100
χ34222-1222-12-2-2-12-1-12-12-12-2-211-2-2-1-1-12-1-1-111-2-2111111002200-20220-22000000-2-200-1-100-2100-122-1001-2-10000110010-1-10100
χ35222-1222-12-2-2-12-1-12-12-12-2-211-2-2-1-1-12-1-1-111-2-211111100-2-200202-20-2-2000000220011002-100-12-21001-210000-1-100-10-110100
χ36222-1222-12-2-2-12-1-12-12-12-2-211-2-2-1-1-12-1-1-111-2-211111100-2-200-20-2202-200000022001100-21001-22-100-1210000-1-100101-10-100
χ3722-1222-12222-1-12-1-12-122-1-12222-1-1-1-12-1-1-1-1-1-122-1-1-1-1220000220220002-1-12200000000-12-1200-12-120000-1-1-10000-1-10-1-1000
χ3822-1222-12222-1-12-1-12-122-1-12222-1-1-1-12-1-1-1-1-1-122-1-1-1-1220000-2-20-2-20002-1-122000000001-21-2001-21-20000-1-1-1000011011000
χ3922-1222-12222-1-12-1-12-122-1-12222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-200002-202-2000-211-2-200000000-121-200-121-200001110000-110-11000
χ4022-1222-12222-1-12-1-12-122-1-12222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-20000-220-22000-211-2-2000000001-2-12001-2-12000011100001-101-1000
χ4122-1222-122-2-2-1-12-1-12-12211-2-2-2-2-1-1-1-12-1-11111-2-21111220000220-2-20002-1-1-2-200000000-12-12001-21-20000-1110000-1-1011000
χ4222-1222-122-2-2-1-12-1-12-12211-2-2-2-2-1-1-1-12-1-11111-2-21111220000-2-20220002-1-1-2-2000000001-21-200-12-120000-1110000110-1-1000
χ4322-1222-122-2-2-1-12-1-12-12211-2-2-2-2-1-1-1-12-1-11111-2-21111-2-200002-20-22000-2112200000000-121-2001-2-1200001-1-10000-1101-1000
χ4422-1222-122-2-2-1-12-1-12-12211-2-2-2-2-1-1-1-12-1-11111-2-21111-2-20000-2202-2000-21122000000001-2-1200-121-200001-1-100001-10-11000
χ452-22220-2-2-2−i2i2222-2-2-2000−i2i2−i2i2−i2i22-200000−i2i2−i2i2−i2i2−i2−i2i2i22-22i−2i2i−2i0000000002-2−i2i22−22−22i−2i2i−2i000000000000000−i2i22−22−200000000
χ462-22220-2-2-2−i2i2222-2-2-2000−i2i2−i2i2−i2i22-200000−i2i2−i2i2−i2i2−i2−i2i2i22-2−2i2i−2i2i0000000002-2−i2i2−22−22−2i2i−2i2i000000000000000−i2i2−22−2200000000
χ472-22220-2-2-2−i2i2222-2-2-2000−i2i2−i2i2−i2i22-200000−i2i2−i2i2−i2i2−i2−i2i2i2-222i−2i−2i2i000000000-22i2−i22−2−222i−2i−2i2i000000000000000i2−i22−2−2200000000
χ482-22220-2-2-2−i2i2222-2-2-2000−i2i2−i2i2−i2i22-200000−i2i2−i2i2−i2i2−i2−i2i2i2-22−2i2i2i−2i000000000-22i2−i2−222−2−2i2i2i−2i000000000000000i2−i2−222−200000000
χ492-22220-2-2-2i2−i2222-2-2-2000i2−i2i2−i2i2−i22-200000i2−i2i2−i2i2−i2i2i2−i2−i22-22i−2i2i−2i0000000002-2i2−i2−22−222i−2i2i−2i000000000000000i2−i2−22−2200000000
χ502-22220-2-2-2i2−i2222-2-2-2000i2−i2i2−i2i2−i22-200000i2−i2i2−i2i2−i2i2i2−i2−i22-2−2i2i−2i2i0000000002-2i2−i22−22−2−2i2i−2i2i000000000000000i2−i22−22−200000000
χ512-22220-2-2-2i2−i2222-2-2-2000i2−i2i2−i2i2−i22-200000i2−i2i2−i2i2−i2i2i2−i2−i2-222i−2i−2i2i000000000-22−i2i2−222−22i−2i−2i2i000000000000000−i2i2−222−200000000
χ522-22220-2-2-2i2−i2222-2-2-2000i2−i2i2−i2i2−i22-200000i2−i2i2−i2i2−i2i2i2−i2−i2-22−2i2i2i−2i000000000-22−i2i22−2−22−2i2i2i−2i000000000000000−i2i22−2−2200000000
χ534444-2-444-2004-2-24-2-2-4-42000000-2-2-4222200000000000000440000000-400000000000-2-200000000000002000000000000000
χ544444-2-444-2004-2-24-2-2-4-42000000-2-2-4222200000000000000-4-40000000400000000000220000000000000-2000000000000000
χ55444-24-44-2400-24-2-24-2-42-4000000-2-22-42220000000000004400000000-40000000000-2-20000000000000020000000000000000
χ56444-24-44-2400-24-2-24-2-42-4000000-2-22-4222000000000000-4-400000000400000000002200000000000000-20000000000000000
χ57444-2-244-2-244-2-21-2-214-2-244-2-2-2-211-2-2111-2-2-2-21111110000000040040000000000000000000-2-20000-2-200000000000100100
χ58444-2-244-2-244-2-21-2-214-2-244-2-2-2-211-2-2111-2-2-2-211111100000000-400-400000000000000000002200002200000000000-100-100
χ59444-2-244-2-2-4-4-2-21-2-214-2-2-4-4222211-2-21112222-1-1-1-1-1-100000000400-40000000000000000000-2-200002200000000000100-100
χ60444-2-244-2-2-4-4-2-21-2-214-2-2-4-4222211-2-21112222-1-1-1-1-1-100000000-40040000000000000000000220000-2-200000000000-100100
χ6144-244-4-24400-2-24-2-242-4-4000000-2-222-422000000000044000000000000-4-2-2000000000000000000000000200000000000000
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χ6444-24-24-24-244-21-2-21-2-24-2-2-244-2-211-21-211-2-211-2-211110000000-400-400000000000000000022000022000000000000-100-1000
χ6544-24-24-24-2-4-4-21-2-21-2-24-222-4-42211-21-21122-1-122-1-1-1-10000000400-4000000000000000000-2-2000022000000000000100-1000
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χ7044-2-244-2-24-4-41-2-21-2-2-2-242222-4-4111-2-211-1-12222-1-1-1-1000000-400400000000000000000220000-2-20000000000000-10010000
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χ928-8-48-404-84−4i24i2-42-44-240002i2−2i2−4i24i22i2−2i22-2000002i2−2i2−i2i22i2−2i2−i2−i2i2i200000000000000000000000000000000000000000000000000000000
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χ968-8-4-4-40444−4i24i2222-2-2-20002i2−2i22i2−2i22i2−2i2-1100033−33−i2i2−i2i2−i2i22ζ5+2ζ7−ζ13−ζ23−ζ5−ζ7+2ζ13+2ζ23−2ζ5−2ζ7+ζ13+ζ23ζ5+ζ7−2ζ13−2ζ2300000000000000000000000000000000000000000000000000000000
χ978-8-4-4-40444−4i24i2222-2-2-20002i2−2i22i2−2i22i2−2i2-11000−3333−i2i2−i2i2−i2i2−ζ5−ζ7+2ζ13+2ζ232ζ5+2ζ7−ζ13−ζ23ζ5+ζ7−2ζ13−2ζ23−2ζ5−2ζ7+ζ13+ζ2300000000000000000000000000000000000000000000000000000000
χ988-8-4-4-404444i2−4i2222-2-2-2000−2i22i2−2i22i2−2i22i2-1100033−33i2−i2i2−i2i2−i2−2ζ5−2ζ7+ζ13+ζ23ζ5+ζ7−2ζ13−2ζ232ζ5+2ζ7−ζ13−ζ23−ζ5−ζ7+2ζ13+2ζ2300000000000000000000000000000000000000000000000000000000
χ998-8-4-4-404444i2−4i2222-2-2-2000−2i22i2−2i22i2−2i22i2-11000−3333i2−i2i2−i2i2−i2ζ5+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.