Finite Group Databasebeta

← Group #72271716

Character table — Group #72271716

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size112222222222244444444444444444488888888161616161616161616161616161616161616161616161616161616161616161616161616161624242424484848484848484848489696
order1222234444612126668888121212242424242424242444444488881212121212121616161616161616242424242424484848484848484848484848484848484444222224448848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1
χ411111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111
χ5111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111111-1-1-111-1111-1-1
χ6111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-111
χ7111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-11-1-1-1-111
χ8111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11111-11111-1-1
χ91111111111111111111111111111111-1-111-1-1-1-11-1-1-111-1-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-111-11-1-11-1-1-11
χ101111111111111111111111111111111-1-111-1-1-1-11-1-1-111-1-111-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11-1-11-111-1111-1
χ111111111111111111111111111111111-1-111-1-1-1-11-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-111-1-1-1-1-1111-1
χ121111111111111111111111111111111-1-111-1-1-1-11-1-1-111-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11-1-111111-1-1-11
χ131111111111111111111111111111111-1-1-1-111-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-111-111-1-11-1
χ141111111111111111111111111111111-1-1-1-111-1-1-11-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1111-1-11-1-111-11
χ151111111111111111111111111111111-1-1-1-111-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1-11-1-11-111-11
χ161111111111111111111111111111111-1-1-1-111-1-1-11-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1111-111-11-1-11-1
χ172222222222222222-2-2-2-2222-2-2-2-2-2-2-2-2222222-2-2-2-222222200000000-2-2-2-2-2-200000000000000000000000000000000
χ182222222222222222-2-2-2-2222-2-2-2-2-2-2-2-222-2-2-2-2-2-22222-2-2-2-200000000-2-2222200000000000000000000000000000000
χ192222222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-222-2-222-22-2-222-2-20000000022-2-22200000000000000000000000000000000
χ202222222222222222-2-2-2-2222-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-222000000002222-2-200000000000000000000000000000000
χ2122222-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ2222222-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-12222222222-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-111111111111111110000000000000000
χ2322222-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-1-111112222-2-2-2-2-1-11111-1-1-1-1-1-1-1-1111111110000000000000000
χ2422222-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-122-2-2-2-222-2-2-1-11111-2-2-2-22222-1-1111111111111-1-1-1-1-1-1-1-10000000000000000
χ2522222-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-22-211-1-11122-2-222-2-211-1-111-1-1-1-11111-1-1-1-111110000000000000000
χ2622222-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-222-2-2-2-22-211-1-111-2-222-2-22211-1-1111111-1-1-1-11111-1-1-1-10000000000000000
χ2722222-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-221111-1-122-2-2-2-2221111-1-1-1-1-1-111111111-1-1-1-10000000000000000
χ2822222-12222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-222-2-2-221111-1-1-2-22222-2-21111-1-11111-1-1-1-1-1-1-1-111110000000000000000
χ2922222-12222-1-1-1-1-1-1-2-2-2-2-1-1-111111111222222-2-2-2-2-1-1-1-1-1-10000000011111133−3−333−3−333−3−333−3−30000000000000000
χ3022222-12222-1-1-1-1-1-1-2-2-2-2-1-1-111111111222222-2-2-2-2-1-1-1-1-1-100000000111111−3−333−3−333−3−333−3−3330000000000000000
χ3122222-12222-1-1-1-1-1-1-2-2-2-2-1-1-11111111122-2-2-2-2-2-222-1-111110000000011-1-1-1-133−3−333−3−3−3−333−3−3330000000000000000
χ3222222-12222-1-1-1-1-1-1-2-2-2-2-1-1-11111111122-2-2-2-2-2-222-1-111110000000011-1-1-1-1−3−333−3−33333−3−333−3−30000000000000000
χ3322222-12222-1-1-1-1-1-1-2-2-2-2-1-1-111111111-2-222-2-222-2211-1-11100000000-1-111-1-133−3−3−3−33333−3−3−3−3330000000000000000
χ3422222-12222-1-1-1-1-1-1-2-2-2-2-1-1-111111111-2-222-2-222-2211-1-11100000000-1-111-1-1−3−33333−3−3−3−33333−3−30000000000000000
χ3522222-12222-1-1-1-1-1-1-2-2-2-2-1-1-111111111-2-2-2-222222-21111-1-100000000-1-1-1-11133−3−3−3−333−3−33333−3−30000000000000000
χ3622222-12222-1-1-1-1-1-1-2-2-2-2-1-1-111111111-2-2-2-222222-21111-1-100000000-1-1-1-111−3−33333−3−333−3−3−3−3330000000000000000
χ37222-2-2222-2-22222-2-2-22-222-2-2-2-222-2-22200000000000000002i−2i0000000000002i−2i2i−2i0000000000002i2i−2i−2i0000200-20000
χ38222-2-2222-2-22222-2-2-22-222-2-2-2-222-2-22200000000000000002i−2i0000000000002i−2i2i−2i000000000000−2i−2i2i2i0000-20020000
χ39222-2-2222-2-22222-2-2-22-222-2-2-2-222-2-2220000000000000000−2i2i000000000000−2i2i−2i2i0000000000002i2i−2i−2i0000-20020000
χ40222-2-2222-2-22222-2-2-22-222-2-2-2-222-2-2220000000000000000−2i2i000000000000−2i2i−2i2i000000000000−2i−2i2i2i0000200-20000
χ4122-22-22-222-2222-22-222-2-2-22-22222-2-2-2-20000000000000000002-2000000000000002-22-2000000002i−2i2i−2i000000002i−2i00
χ4222-22-22-222-2222-22-222-2-2-22-22222-2-2-2-20000000000000000002-2000000000000002-22-200000000−2i2i−2i2i00000000−2i2i00
χ4322-22-22-222-2222-22-222-2-2-22-22222-2-2-2-2000000000000000000-2200000000000000-22-22000000002i−2i2i−2i00000000−2i2i00
χ4422-22-22-222-2222-22-222-2-2-22-22222-2-2-2-2000000000000000000-2200000000000000-22-2200000000−2i2i−2i2i000000002i−2i00
χ4522-2-222-22-22222-2-222-2-22-2-2222-2-2-2-2222-200002-2002-20000000000002-200000000000000000000000002-2200-200000
χ4622-2-222-22-22222-2-222-2-22-2-2222-2-2-2-2222-200002-2002-20000000000002-20000000000000000000000000-22-200200000
χ4722-2-222-22-22222-2-222-2-22-2-2222-2-2-2-222-220000-2200-22000000000000-2200000000000000000000000002-2-200200000
χ4822-2-222-22-22222-2-222-2-22-2-2222-2-2-2-222-220000-2200-22000000000000-220000000000000000000000000-22200-200000
χ4922-2-222-22-22222-2-22-222-2-2-22-2-22222-2-22-20000-22002-2000000000000-22000000000000000000002-2-2220000-2000000
χ5022-2-222-22-22222-2-22-222-2-2-22-2-22222-2-22-20000-22002-2000000000000-2200000000000000000000-222-2-200002000000
χ5122-2-222-22-22222-2-22-222-2-2-22-2-22222-2-2-2200002-200-220000000000002-2000000000000000000002-2-22-200002000000
χ5222-2-222-22-22222-2-22-222-2-2-22-2-22222-2-2-2200002-200-220000000000002-200000000000000000000-222-220000-2000000
χ53444444-4-4-4-44-4-44440000-4-4-40000000000004-4000000004-40000000000000000000000000000000000000000000000
χ54444444-4-4-4-44-4-44440000-4-4-4000000000000-4400000000-440000000000000000000000000000000000000000000000
χ5544444-2-4-4-4-4-222-2-2-2000022223−2323−2323−2323−2300004-400000000-2200000000000023−2300000000000000000000000000000000
χ5644444-2-4-4-4-4-222-2-2-2000022223−2323−2323−2323−230000-44000000002-2000000000000−232300000000000000000000000000000000
χ5744444-2-4-4-4-4-222-2-2-20000222−2323−2323−2323−232300004-400000000-22000000000000−232300000000000000000000000000000000
χ5844444-2-4-4-4-4-222-2-2-20000222−2323−2323−2323−23230000-44000000002-200000000000023−2300000000000000000000000000000000
χ59444-4-4444-4-44444-4-44-44-44-4-444-4-444-4-400000000000000000000000000000000000000000000000000000000000000
χ60444-4-44-4-4444-4-44-4-40000-44400000000000000000000000000000022−2200000000000000000022−2222−220000000000000000
χ61444-4-44-4-4444-4-44-4-40000-444000000000000000000000000000000−2222000000000000000000−2222−22220000000000000000
χ62444-4-4-244-4-4-2-2-2-2224-44-4-222-2-222-2-222000000000000000000000000000000−2i32i32i3−2i30000000000000000000000000000
χ63444-4-4-244-4-4-2-2-2-2224-44-4-222-2-222-2-2220000000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000
χ64444-4-4-244-4-4-2-2-2-222-44-44-22222-2-222-2-200000000000000004i−4i000000000000−2i2i−2i2i0000000000000000000000000000
χ65444-4-4-244-4-4-2-2-2-222-44-44-22222-2-222-2-20000000000000000−4i4i0000000000002i−2i2i−2i0000000000000000000000000000
χ66444-4-4-2-4-444-222-22200002-2-223−23−232323−23−2323000000000000000000000022−220000000000000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000
χ67444-4-4-2-4-444-222-22200002-2-223−23−232323−23−23230000000000000000000000−2222000000000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ230000000000000000
χ68444-4-4-2-4-444-222-22200002-2-2−232323−23−232323−23000000000000000000000022−220000000000000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000
χ69444-4-4-2-4-444-222-22200002-2-2−232323−23−232323−230000000000000000000000−2222000000000000000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000
χ7044-44-444-4-444-4-4-44-400004-44000000000000000000000000000022−22000000000000000022−2222−2200000000000000000000
χ7144-44-444-4-444-4-4-44-400004-440000000000000000000000000000−22220000000000000000−2222−222200000000000000000000
χ7244-44-44-444-4444-44-4-4-444-44-4-4-4-4-4444400000000000000000000000000000000000000000000000000000000000000
χ7344-44-4-24-4-44-2222-220000-22-223−2323−23−2323−23230000000000000000000022−2200000000000000002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000
χ7444-44-4-24-4-44-2222-220000-22-223−2323−23−2323−232300000000000000000000−22220000000000000000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000
χ7544-44-4-24-4-44-2222-220000-22-2−2323−232323−2323−230000000000000000000022−2200000000000000002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300000000000000000000
χ7644-44-4-24-4-44-2222-220000-22-2−2323−232323−2323−2300000000000000000000−22220000000000000000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2300000000000000000000
χ7744-44-4-2-444-4-2-2-22-2244-4-42-22-2-2-2-222220000000000000000004-400000000000000-22-22000000000000000000000000
χ7844-44-4-2-444-4-2-2-22-2244-4-42-22-2-2-2-22222000000000000000000-44000000000000002-22-2000000000000000000000000
χ7944-44-4-2-444-4-2-2-22-22-4-4442-222222-2-2-2-2000000000000000000000000000000000023−23−2323000000000000000000000000
χ8044-44-4-2-444-4-2-2-22-22-4-4442-222222-2-2-2-20000000000000000000000000000000000−232323−23000000000000000000000000
χ8144-4-4444-44-44-4-4-4-44000044-400000000004-4000000004-4000000000000000000000000000000000000000000000000
χ8244-4-4444-44-44-4-4-4-44000044-40000000000-4400000000-44000000000000000000000000000000000000000000000000
χ8344-4-44-24-44-4-22222-20000-2-2223−23−2323−232323−23004-400000000-2200000000000023−230000000000000000000000000000000000
χ8444-4-44-24-44-4-22222-20000-2-2223−23−2323−232323−2300-44000000002-2000000000000−23230000000000000000000000000000000000
χ8544-4-44-24-44-4-22222-20000-2-22−232323−2323−23−2323004-400000000-22000000000000−23230000000000000000000000000000000000
χ8644-4-44-24-44-4-22222-20000-2-22−232323−2323−23−232300-44000000002-200000000000023−230000000000000000000000000000000000
χ8744-4-44-2-44-44-2-2-222-24-4-4422-2-2-22222-2-24-400004-400-22000000000000-22000000000000000000000000000000000000
χ8844-4-44-2-44-44-2-2-222-24-4-4422-2-2-22222-2-2-440000-44002-20000000000002-2000000000000000000000000000000000000
χ8944-4-44-2-44-44-2-2-222-2-444-422-222-2-2-2-2224-40000-4400-220000000000002-2000000000000000000000000000000000000
χ9044-4-44-2-44-44-2-2-222-2-444-422-222-2-2-2-222-4400004-4002-2000000000000-22000000000000000000000000000000000000
χ9116-16000160000-160000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9216-16000-80000883−8300000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9316-16000-800008−838300000000000000000000000000000000000000000000000000000000000000000000000000000000

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