Finite Group Databasebeta

← Group #10768841

Character table — Group #10768841

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881616161616161616161624242424242424242424242424242424
order12222222344666244466661212121212124444688881224242424242424248812121212242424242444444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-11-1-1-1-11111
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-11111-1-1-1-1
χ71111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1111111-1-11-1-111111-1-1-1-1
χ81111111111111111111111111111-1-1-1-11-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-111-1-1-1-1-11111
χ91111-1-1111-1-1111-1-11111-1-1-1-111111-11-1-111-1-1-11111-1-1-1-11-11-11-111-1-11-11-1-11-1111-1-111-1-1
χ101111-1-1111-1-1111-1-11111-1-1-1-111111-11-1-111-1-1-11111-1-1-1-11-11-11-111-1-1-11-111-11-1-1-111-1-111
χ111111-1-1111-1-1111-1-11111-1-1-1-111111-11-1-1-1-111-1-1-1-1-11111-111-11-1-1-1111-11-1-11-11-1-111-1-111
χ121111-1-1111-1-1111-1-11111-1-1-1-111111-11-1-1-1-111-1-1-1-1-11111-111-11-1-1-111-11-111-11-111-1-111-1-1
χ131111-1-1111-1-1111-1-11111-1-1-1-11111-11-11-111-1-1-11111-1-1-1-1-11-11-11-1-1111-1-11-1-111-1-11111-1-1
χ141111-1-1111-1-1111-1-11111-1-1-1-11111-11-11-111-1-1-11111-1-1-1-1-11-11-11-1-111-111-111-1-111-1-1-1-111
χ151111-1-1111-1-1111-1-11111-1-1-1-11111-11-11-1-1-111-1-1-1-1-111111-1-11-1111-1-11-1-11-1-11111-1-1-1-111
χ161111-1-1111-1-1111-1-11111-1-1-1-11111-11-11-1-1-111-1-1-1-1-111111-1-11-1111-1-1-111-111-1-1-1-11111-1-1
χ17222222222-2-22222-2-2-22222-2-2-2-2-2-22-2-2220000-20000000000-222-200000000000000000000
χ18222222222-2-22222-2-2-22222-2-2-2-2-2-2-222-220000-200000000002-2-2200000000000000000000
χ1922222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-12222-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000000000000
χ2022222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-2-2-2-2-111111111-2-2-1-1-1-111110000000000000000
χ2122222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-12222-1-1-1-1-1-1-1-1-1-2-2111111110000000000000000
χ2222222222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-2-2-2-2-111111111221111-1-1-1-10000000000000000
χ2322222222-1-2-2-1-1-12-2-2-2-1-1-1-11111112-2-22-10000133−3−333−3−3001-1-113−33−30000000000000000
χ2422222222-1-2-2-1-1-12-2-2-2-1-1-1-11111112-2-22-100001−3−333−3−333001-1-11−33−330000000000000000
χ2522222222-1-2-2-1-1-12-2-2-2-1-1-1-1111111-222-2-10000133−3−333−3−300-111-1−33−330000000000000000
χ2622222222-1-2-2-1-1-12-2-2-2-1-1-1-1111111-222-2-100001−3−333−3−33300-111-13−33−30000000000000000
χ27222222-2-2222222-2-22-2-2-2222222-2-20000-20000-200000000000000000000220-2-2000000000
χ28222222-2-2222222-2-22-2-2-2222222-2-20000-20000-200000000000000000000-2-2022000000000
χ29222222-2-22-2-2222-22-22-2-222-2-2-2-2220000-2000020000000000000000002200-200-200000000
χ30222222-2-22-2-2222-22-22-2-222-2-2-2-2220000-200002000000000000000000-2-200200200000000
χ312222-2-222222222-22-2-222-2-222-2-2-2-222-2-2-2000020000000000-2-22200000000000000000000
χ322222-2-222222222-22-2-222-2-222-2-2-2-2-2-222-200002000000000022-2-200000000000000000000
χ332222-2-222-122-1-1-1-22-2-2-1-111-1-1111122-2-210000-133−3−3−3−3330011-1-13−3−330000000000000000
χ342222-2-222-122-1-1-1-22-2-2-1-111-1-1111122-2-210000-1−3−33333−3−30011-1-1−333−30000000000000000
χ352222-2-222-122-1-1-1-22-2-2-1-111-1-11111-2-22210000-133−3−3−3−33300-1-111−333−30000000000000000
χ362222-2-222-122-1-1-1-22-2-2-1-111-1-11111-2-22210000-1−3−33333−3−300-1-1113−3−330000000000000000
χ372222-2-222-1-2-2-1-1-1-2-222-1-11111-1-1-1-12-22-2122-2-21-1-1-1-111112-2-11-11-1-1110000000000000000
χ382222-2-222-1-2-2-1-1-1-2-222-1-11111-1-1-1-12-22-21-2-22211111-1-1-1-1-22-11-1111-1-10000000000000000
χ392222-2-222-1-2-2-1-1-1-2-222-1-11111-1-1-1-1-22-22122-2-21-1-1-1-11111-221-11-111-1-10000000000000000
χ402222-2-222-1-2-2-1-1-1-2-222-1-11111-1-1-1-1-22-221-2-22211111-1-1-1-12-21-11-1-1-1110000000000000000
χ412222-2-2-2-22222222-2-22-2-2-2-222-2-222000020000-20000000000000000002-200200-200000000
χ422222-2-2-2-22222222-2-22-2-2-2-222-2-222000020000-2000000000000000000-2200-200200000000
χ432222-2-2-2-22-2-2222222-2-2-2-2-2-2-222-2-20000200002000000000000000000002-20-22000000000
χ442222-2-2-2-22-2-2222222-2-2-2-2-2-2-222-2-2000020000200000000000000000000-2202-2000000000
χ45444444-4-4-244-2-2-2-4-44-422-2-2-2-2-2-22200002000020000000000000000000000000000000000
χ46444444-4-4-2-4-4-2-2-2-44-4422-2-22222-2-2000020000-20000000000000000000000000000000000
χ474444-4-4-4-4-244-2-2-24-4-442222-2-222-2-20000-2000020000000000000000000000000000000000
χ484444-4-4-4-4-2-4-4-2-2-2444-4222222-2-2220000-20000-20000000000000000000000000000000000
χ4944-4-44-4004004-4-40000004-400000000000000000000000000000000000000000000002-22-2
χ5044-4-44-4004004-4-40000004-40000000000000000000000000000000000000000000000-22-22
χ5144-4-4-44004004-4-4000000-4400000000000000000000000000000000000000000000002-2-22
χ5244-4-4-44004004-4-4000000-440000000000000000000000000000000000000000000000-222-2
χ534-44-4000044-4-4-44000000004-400000000000000000000000000000000000000002i−2i2i−2i0000
χ544-44-4000044-4-4-44000000004-40000000000000000000000000000000000000000−2i2i−2i2i0000
χ554-44-400004-44-4-4400000000-4400000000000000000000000000000000000000002i−2i−2i2i0000
χ564-44-400004-44-4-4400000000-440000000000000000000000000000000000000000−2i2i2i−2i0000
χ574-4-44004-4400-44-400004-4000000000000000−2i22i200000−2i22i2−2i22i200000000000000000000000000
χ584-4-44004-4400-44-400004-40000000000000002i2−2i2000002i2−2i22i2−2i200000000000000000000000000
χ594-4-44004-4-2002-220000-22000023−2323−230000000−2i22i2000002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000
χ604-4-44004-4-2002-220000-22000023−2323−2300000002i2−2i200000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000
χ614-4-44004-4-2002-220000-220000−2323−23230000000−2i22i2000002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000
χ624-4-44004-4-2002-220000-220000−2323−232300000002i2−2i200000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000
χ634-4-4400-44400-44-40000-440000000000000−2i22i2000−2i22i2−2i22i2000000000000000000000000000000
χ644-4-4400-44400-44-40000-4400000000000002i2−2i20002i2−2i22i2−2i2000000000000000000000000000000
χ654-4-4400-44-2002-2200002-2000023−23−232300000−2i22i20002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7000000000000000000000000000000
χ664-4-4400-44-2002-2200002-2000023−23−2323000002i2−2i2000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ7000000000000000000000000000000
χ674-4-4400-44-2002-2200002-20000−232323−2300000−2i22i20002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23000000000000000000000000000000
χ684-4-4400-44-2002-2200002-20000−232323−23000002i2−2i2000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ23000000000000000000000000000000
χ6988-8-88-800-400-444000000-4400000000000000000000000000000000000000000000000000
χ7088-8-8-8800-400-4440000004-400000000000000000000000000000000000000000000000000
χ718-88-80000-48-844-400000000-44000000000000000000000000000000000000000000000000
χ728-88-80000-4-8844-4000000004-4000000000000000000000000000000000000000000000000

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