Finite Group Databasebeta

← Group #10833338

Character table — Group #10833338

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size111122222222222222444444444444444488888888888888888888888888121212121616161616242424242424242424244848
order12222234444666121212122244668888121224242424244466888812121212121224242424242424242424224468122424224444448848
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1111111-1-1-1-111111-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111-1-1111111-1-1-1-111111-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ5111111111111111111111111-1-11111-1-1-1-111-1-111-1-1-1111-1-1-1-1-1-1-1-1-1-1111111111-11-1-111-1-1-1-11111-1-1
χ6111111111111111111111111-1-11111-1-1-1-111-1-111-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1-1-1-11111-1-1-1-111
χ7111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-11-111-1-1-1-1-1-111-1-111
χ8111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111-1-111-1-1
χ9111111111111111111-1-1-1-1111111111111-1-111-1-11-1-11-1-1111111-1-1-1-111111111-1-1-1-1-1-1-111-1-1-1-111-11
χ10111111111111111111-1-1-1-1111111111111-1-111-1-11-1-11-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111-1-11-1
χ11111111111111111111-1-1-1-11111-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-11-1
χ12111111111111111111-1-1-1-11111-1-111111111-1-1-1-11-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1111111-11
χ13111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111111111-11-111-1-1-1-111-1-1111-1
χ14111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1111111-1-111-1-1-11
χ15111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-111-1-1-11111-1-11111-1-1-1-111111-11-1-111-1-111-1-1-1-1-11
χ16111111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-111-1-111111-1
χ17222222-12222-1-1-1-1-1-1-12222-1-12222-1-1-1-1-1-12222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-12-1-1-1000000000000
χ18222222-12222-1-1-1-1-1-1-12222-1-122-2-2-1-1-1-1-1-1-2-2-2-2-1-1222-2-1-11111-1-1-1-1-1-1111100001-2111000000000000
χ19222222-12222-1-1-1-1-1-1-12222-1-1-2-222-1-1111122-2-2-1-1-2-2-22-1-11111111111-1-1-1-10000-1-2-111000000000000
χ20222222-12222-1-1-1-1-1-1-12222-1-1-2-2-2-2-1-11111-2-222-1-1-2-2-2-2-1-1-1-1-1-111111111110000121-1-1000000000000
χ21222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-12222-1-1-1-1-1-1-2-222112-2-2211-1-1-1-1-1-11111-1-1-1-100001-2111000000000000
χ22222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-122-2-2-1-1-1-1-1-122-2-2112-2-2-2111111-1-1111111110000-12-1-1-1000000000000
χ23222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-222-1-11111-2-2-2-211-222211111111-1-1-1-1-1-1-1-10000121-1-1000000000000
χ24222222-12222-1-1-1-1-1-1-1-2-2-2-2-1-1-2-2-2-2-1-11111222211-222-211-1-1-1-111-1-1-1-111110000-1-2-111000000000000
χ252222-2-222-2-22222-2-2-2-222-2-2-2-20022220000-220022000-2-2-2000000000022-2-20000-20200000000000000
χ262222-2-222-2-22222-2-2-2-222-2-2-2-200-2-22200002-200220002-2-20000000000-2-222000020-200000000000000
χ272222-2-222-2-22222-2-2-2-2-2-222-2-200222200002-200-2-2000-222000000000022-2-2000020-200000000000000
χ282222-2-222-2-22222-2-2-2-2-2-222-2-200-2-2220000-2200-2-20002220000000000-2-2220000-20200000000000000
χ292222-2-22-222-222222220000-2-22200-2-22222000000-2000000000-2-20000000022-2-200000002-200000000
χ302222-2-22-222-222222220000-2-22200-2-22222000000-2000000000-2-200000000-2-2220000000-2200000000
χ312222-2-22-222-222222220000-2-2-2-200-2-2-2-2-2-20000002000000000220000000022-2-20000000-2200000000
χ322222-2-22-222-222222220000-2-2-2-200-2-2-2-2-2-200000020000000002200000000-2-22200000002-200000000
χ332222-2-2-12-2-22-1-1-1111122-2-2110022-1-133−3−3-2200-1-1000-21133−3−33−333−3−3-1-111000010-13−3000000000000
χ342222-2-2-12-2-22-1-1-1111122-2-2110022-1-1−3−333-2200-1-1000-211−3−333−33−3−333-1-111000010-1−33000000000000
χ352222-2-2-12-2-22-1-1-1111122-2-21100-2-2-1-133−3−32-200-1-1000211−3−3333−333−3−311-1-10000-101−33000000000000
χ362222-2-2-12-2-22-1-1-1111122-2-21100-2-2-1-1−3−3332-200-1-100021133−3−3−33−3−33311-1-10000-1013−3000000000000
χ372222-2-2-12-2-22-1-1-11111-2-222110022-1-133−3−32-20011000-2-1-133−3−33−3−3−333-1-1110000-101−33000000000000
χ382222-2-2-12-2-22-1-1-11111-2-222110022-1-1−3−3332-20011000-2-1-1−3−333−3333−3−3-1-1110000-1013−3000000000000
χ392222-2-2-12-2-22-1-1-11111-2-2221100-2-2-1-133−3−3-2200110002-1-1−3−3333−3−3−33311-1-1000010-13−3000000000000
χ402222-2-2-12-2-22-1-1-11111-2-2221100-2-2-1-1−3−333-2200110002-1-133−3−3−3333−3−311-1-1000010-1−33000000000000
χ412-2-222-2222-2-2-2-2222-2-200002-200002-2000000000002i−2i0000000002i−2i2i−2i00002-22-20000000002i−2i000000
χ422-2-222-2222-2-2-2-2222-2-200002-200002-2000000000002i−2i0000000002i−2i2i−2i0000-22-22000000000−2i2i000000
χ432-2-222-2222-2-2-2-2222-2-200002-200002-200000000000−2i2i000000000−2i2i−2i2i00002-22-2000000000−2i2i000000
χ442-2-222-2222-2-2-2-2222-2-200002-200002-200000000000−2i2i000000000−2i2i−2i2i0000-22-220000000002i−2i000000
χ452-2-222-22-2-222-2-22-2-2222-22-22-20000-22000000002-200002-2000000000000000000000002-20000002-200
χ462-2-222-22-2-222-2-22-2-2222-22-22-20000-22000000002-200002-200000000000000000000000-22000000-2200
χ472-2-222-22-2-222-2-22-2-222-22-222-20000-2200000000-220000-22000000000000000000000002-2000000-2200
χ482-2-222-22-2-222-2-22-2-222-22-222-20000-2200000000-220000-2200000000000000000000000-220000002-200
χ492-2-22-222-22-22-2-2222-2-22-2-22-220000-22000000002-20000-22000000000000002-2-22000000000002-20000
χ502-2-22-222-22-22-2-2222-2-22-2-22-220000-22000000002-20000-2200000000000000-222-200000000000-220000
χ512-2-22-222-22-22-2-2222-2-2-222-2-220000-2200000000-2200002-2000000000000002-2-2200000000000-220000
χ522-2-22-222-22-22-2-2222-2-2-222-2-220000-2200000000-2200002-200000000000000-222-2000000000002-20000
χ534444444-4-4-4-4444-4-4-4-40000440000-4-4000000000000000000000000000000000000000000000000000
χ54444444-2-4-4-4-4-2-2-222220000-2-20000222323−23−230000000000000000−232300000000000000000000000000000
χ55444444-2-4-4-4-4-2-2-222220000-2-2000022−23−232323000000000000000023−2300000000000000000000000000000
χ564444-4-4-2-444-4-2-2-2-2-2-2-2000022440022-2-2-2-2000000-40000000002200000000000000000000000000000
χ574444-4-4-2-444-4-2-2-2-2-2-2-2000022-4-4002222220000004000000000-2-200000000000000000000000000000
χ584-44-400400004-4-40000000000−2i22i2−2i22i200−2i22i2−2i22i2002-2000000002-22-2000000−2i22i200000000000000000000000
χ594-44-400400004-4-40000000000−2i22i22i2−2i200−2i22i2−2i22i200-2200000000-22-220000002i2−2i200000000000000000000000
χ604-44-400400004-4-400000000002i2−2i2−2i22i2002i2−2i22i2−2i200-2200000000-22-22000000−2i22i200000000000000000000000
χ614-44-400400004-4-400000000002i2−2i22i2−2i2002i2−2i22i2−2i2002-2000000002-22-20000002i2−2i200000000000000000000000
χ624-44-400-20000-22223−2323−23000000−2i22i2−2i22i2002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23002-200000000−1−31+3−1+31−3000000i2−i2i6−i6000000000000000000000
χ634-44-400-20000-22223−2323−23000000−2i22i22i2−2i2002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300-22000000001+3−1−31−3−1+3000000−i2i2−i6i6000000000000000000000
χ644-44-400-20000-22223−2323−230000002i2−2i2−2i22i200−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300-22000000001+3−1−31−3−1+3000000i2−i2i6−i6000000000000000000000
χ654-44-400-20000-22223−2323−230000002i2−2i22i2−2i200−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23002-200000000−1−31+3−1+31−3000000−i2i2−i6i6000000000000000000000
χ664-44-400-20000-222−2323−2323000000−2i22i2−2i22i2002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7002-200000000−1+31−3−1−31+3000000i2−i2−i6i6000000000000000000000
χ674-44-400-20000-222−2323−2323000000−2i22i22i2−2i2002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700-22000000001−3−1+31+3−1−3000000−i2i2i6−i6000000000000000000000
χ684-44-400-20000-222−2323−23230000002i2−2i2−2i22i200−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700-22000000001−3−1+31+3−1−3000000i2−i2−i6i6000000000000000000000
χ694-44-400-20000-222−2323−23230000002i2−2i22i2−2i200−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7002-200000000−1+31−3−1−31+3000000−i2i2i6−i6000000000000000000000
χ704-4-444-4-244-4-422-2-2-2220000-220000-22000000000004i−4i000000000−2i2i−2i2i0000000000000000000000000
χ714-4-444-4-244-4-422-2-2-2220000-220000-2200000000000−4i4i0000000002i−2i2i−2i0000000000000000000000000
χ724-4-444-4-2-4-44422-222-2-24-44-4-2200002-200000000-220000-2200000000000000000000000000000000000
χ734-4-444-4-2-4-44422-222-2-2-44-44-2200002-2000000002-200002-200000000000000000000000000000000000
χ744-4-44-4444-44-4-4-44-4-4440000-4400004-4000000000000000000000000000000000000000000000000000
χ754-4-44-44-24-44-422-222-2-200002-20000-220000000000000000000000−2i32i32i3−2i30000000000000000000000000
χ764-4-44-44-24-44-422-222-2-200002-20000-2200000000000000000000002i3−2i3−2i32i30000000000000000000000000
χ774-4-44-44-2-44-4422-2-2-2224-4-442-200002-200000000-2200002-200000000000000000000000000000000000
χ784-4-44-44-2-44-4422-2-2-222-444-42-200002-2000000002-20000-2200000000000000000000000000000000000
χ7988-8-80080000-88-80000000000000000000000000000000000000000000000000000000000000000000
χ8088-8-800-400004-4443−43−4343000000000000000000000000000000000000000000000000000000000000000
χ8188-8-800-400004-44−434343−43000000000000000000000000000000000000000000000000000000000000000

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