Finite Group Databasebeta

← Group #13167747

Character table — Group #13167747

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1122222222244444444444444488888888888888888999999121212121212181818181818181818181818181818242424242424242424242424363636363636363636484848484848108108
order123334666883336661212122424242424243612121212122424242424242424242422222222244444466666688888866666612121212121212121224242424242466612121224
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
χ3111111111111111111111111111111111111111111111-1-1-1-111-111-11-1-111-1-1-1-111-1-1-1-11111-1-11111-1-11-1-111-1-1-1-111-111-1-1-1
χ4111111111111111111111111111111111111111111111-1-1-1-1-1-11-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1111-1-111-1-1-1-1-1-11-1-1111
χ51111111111111111111111111111111111111111111-1-111-1-11-111-11-11-1-1-111-1-1-1-111-1-111-1-11111-1-111-11-1-1-111-1-11-111-11-1-1
χ61111111111111111111111111111111111111111111-1-111-1-1-11-1-11-1-11-1-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-1-11-1-1-111-1-1-11-1-11-111
χ71111111111111111111111111111111111111111111-1-1-1-1111-1-11-1-1-1-11-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-1-1-1-1111-1-11-1-111
χ81111111111111111111111111111111111111111111-1-1-1-111-111-111-1-11-1-1-1-111-1-1-1-111-1-11111-1-11111-1-11-1-1-1-111-111-111-1-1
χ9111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111111-1-1-1111111111-1-1-1-1-1-1111111-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-11-1
χ10111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1111-11
χ11111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-111-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-11-11
χ12111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-11-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-11-1-1-1-11111-1-1111-11-1
χ13111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-11-11-1-11-1-1-111-1-111-1-11111-1-111-1-111-1-1-11-111-1-1111-11-11-1-11
χ14111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-11-11-11-1-1-111-1-111-1-111-1-111-1-111-1-111-11-111-1-111-11-11-111-1
χ15111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-11-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-111111-1-11-1-1-1111-1
χ16111111111-1-1111111111-1-1-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111-1-1-1-11-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-111111-1-1-1111-1-1-11
χ1722222-222200222222-2-2-200000022-2-2-2-2-20000000000222222000000-2-2-2222222000000000000000000-2-2-200000000000000
χ1822222-222200222222-2-2-200000022-2-2-2-2-2000000000022-2-2-2-2000000-22222-2-2-2-2000000000000000000-22200000000000000
χ1922222-222200222222-2-2-200000022-2-2-2-2-20000000000-2-222-2-20000002-22-2-222-2-20000000000000000002-2200000000000000
χ2022222-222200222222-2-2-200000022-2-2-2-2-20000000000-2-2-2-22200000022-2-2-2-2-22200000000000000000022-200000000000000
χ212222-1222-1222-1-12-1-122-12222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-10000220220220020000-1-1000022002-12-1002-12-100-10000-1-10-1-10-1-100
χ222222-1222-1222-1-12-1-122-12222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-10000220-2-20-2-20020000-1-100002200-21-2100-21-2100-10000-1-101101100
χ232222-1222-1222-1-12-1-122-12222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-10000-2-202-202-200-20000110000-2-2002-1-21002-1-210010000110-110-1100
χ242222-1222-1222-1-12-1-122-12222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-10000-2-20-220-2200-20000110000-2-200-212-100-212-100100001101-101-100
χ252222-1222-1-2-22-1-12-1-122-1-2-2-2-211-1-12-1-1-1-1-2-2111111110000220220-2-20020000-1-10000-2-2002-12-100-21-2100-10000110-1-101100
χ262222-1222-1-2-22-1-12-1-122-1-2-2-2-211-1-12-1-1-1-1-2-2111111110000220-2-20220020000-1-10000-2-200-21-21002-12-100-10000110110-1-100
χ272222-1222-1-2-22-1-12-1-122-1-2-2-2-211-1-12-1-1-1-1-2-2111111110000-2-202-20-2200-2000011000022002-1-2100-212-10010000-1-10-1101-100
χ282222-1222-1-2-22-1-12-1-122-1-2-2-2-211-1-12-1-1-1-1-2-2111111110000-2-20-2202-200-200001100002200-212-1002-1-210010000-1-101-10-1100
χ29222-1222-1222-12-1-12-12-1222-1-122-1-1-12-1-1-1-1-122-1-1-1-1-1-100220020220202000-1-1000022002-100-122-100-120-1000-1-100-10-1-10-100
χ30222-1222-1222-12-1-12-12-1222-1-122-1-1-12-1-1-1-1-122-1-1-1-1-1-1002200-20-2-20-202000-1-100002200-21001-2-21001-20-1000-1-10010110100
χ31222-1222-1222-12-1-12-12-1222-1-122-1-1-12-1-1-1-1-122-1-1-1-1-1-100-2-20020-220-20-2000110000-2-2002-1001-22-1001-2010001100-101-10100
χ32222-1222-1222-12-1-12-12-1222-1-122-1-1-12-1-1-1-1-122-1-1-1-1-1-100-2-200-202-2020-2000110000-2-200-2100-12-2100-1201000110010-110-100
χ33222-1222-12-2-2-12-1-12-12-12-2-211-2-2-1-1-12-1-1-111-2-2111111002200202-20-202000-1-10000-2-2002-100-12-21001-20-10001100-10-110100
χ34222-1222-12-2-2-12-1-12-12-12-2-211-2-2-1-1-12-1-1-111-2-2111111002200-20-220202000-1-10000-2-200-21001-22-100-120-10001100101-10-100
χ35222-1222-12-2-2-12-1-12-12-12-2-211-2-2-1-1-12-1-1-111-2-211111100-2-20020-2-2020-200011000022002-1001-2-2100-1201000-1-100-10110-100
χ36222-1222-12-2-2-12-1-12-12-12-2-211-2-2-1-1-12-1-1-111-2-211111100-2-200-20220-20-20001100002200-2100-122-1001-201000-1-10010-1-10100
χ3722-1222-12222-1-12-1-12-122-1-12222-1-1-1-12-1-1-1-1-1-122-1-1-1-1220000220220200-1-10000220000-12-1200-12-1200-100-1-10000-1-10-1-1000
χ3822-1222-12222-1-12-1-12-122-1-12222-1-1-1-12-1-1-1-1-1-122-1-1-1-1220000-2-20-2-20200-1-100002200001-21-2001-21-200-100-1-1000011011000
χ3922-1222-12222-1-12-1-12-122-1-12222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-200002-202-20-200110000-2-20000-121-200-121-200100110000-110-11000
χ4022-1222-12222-1-12-1-12-122-1-12222-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-20000-220-220-200110000-2-200001-2-12001-2-12001001100001-101-1000
χ4122-1222-122-2-2-1-12-1-12-12211-2-2-2-2-1-1-1-12-1-11111-2-21111220000220-2-20200-1-10000-2-20000-12-12001-21-200-100110000-1-1011000
χ4222-1222-122-2-2-1-12-1-12-12211-2-2-2-2-1-1-1-12-1-11111-2-21111220000-2-20220200-1-10000-2-200001-21-200-12-1200-100110000110-1-1000
χ4322-1222-122-2-2-1-12-1-12-12211-2-2-2-2-1-1-1-12-1-11111-2-21111-2-200002-20-220-200110000220000-121-2001-2-1200100-1-10000-1101-1000
χ4422-1222-122-2-2-1-12-1-12-12211-2-2-2-2-1-1-1-12-1-11111-2-21111-2-20000-2202-20-2001100002200001-2-1200-121-200100-1-100001-10-11000
χ452-22220-2-2-2−i2i2222-2-2-2000−i2i2−i2i2−i2i22-200000−i2i2−i2i2−i2i2−i2−i2i2i22-22-22-20000000002-22-22-2−i2i2−i2i2−i2i2000000000000000−i2i2−i2i2−i2i200000000
χ462-22220-2-2-2−i2i2222-2-2-2000−i2i2−i2i2−i2i22-200000−i2i2−i2i2−i2i2−i2−i2i2i22-2-22-220000000002-2-22-22−i2i2i2−i2i2−i2000000000000000−i2i2i2−i2i2−i200000000
χ472-22220-2-2-2−i2i2222-2-2-2000−i2i2−i2i2−i2i22-200000−i2i2−i2i2−i2i2−i2−i2i2i2-222-2-22000000000-222-2-22i2−i2−i2i2i2−i2000000000000000i2−i2−i2i2i2−i200000000
χ482-22220-2-2-2−i2i2222-2-2-2000−i2i2−i2i2−i2i22-200000−i2i2−i2i2−i2i2−i2−i2i2i2-22-222-2000000000-22-222-2i2−i2i2−i2−i2i2000000000000000i2−i2i2−i2−i2i200000000
χ492-22220-2-2-2i2−i2222-2-2-2000i2−i2i2−i2i2−i22-200000i2−i2i2−i2i2−i2i2i2−i2−i22-22-22-20000000002-22-22-2i2−i2i2−i2i2−i2000000000000000i2−i2i2−i2i2−i200000000
χ502-22220-2-2-2i2−i2222-2-2-2000i2−i2i2−i2i2−i22-200000i2−i2i2−i2i2−i2i2i2−i2−i22-2-22-220000000002-2-22-22i2−i2−i2i2−i2i2000000000000000i2−i2−i2i2−i2i200000000
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χ522-22220-2-2-2i2−i2222-2-2-2000i2−i2i2−i2i2−i22-200000i2−i2i2−i2i2−i2i2i2−i2−i2-22-222-2000000000-22-222-2−i2i2−i2i2i2−i2000000000000000−i2i2−i2i2i2−i200000000
χ534444-2-444-2004-2-24-2-2-4-42000000-2-2-42222000000000000004400000000-40000-2-200000000000000000000200000000000000
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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
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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.