Finite Group Databasebeta

← Group #10691052

Character table — Group #10691052

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444444444444444444444488888888888888888888888888242424242424242448484848
order1222223444444666121212122244444666666888812121212121212121212242424242424242444888888121212121212242424242424242424242424888888884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-11-1-11111-1-1-1-11111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111-1-11-1-11111-1-1-1-11111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111111111111111-1-11-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ91111-1-111-1-1-11-1111-1-1-1-1111-1-11-1-1-11111ii−i−i1111-1-1-1-1-1-1iiii−i−i−i−i-11i−iii−i−i1-111-1-1ii−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ101111-1-111-1-1-11-1111-1-1-1-1111-1-11-1-1-11111ii−i−i1111-1-1-1-1-1-1iiii−i−i−i−i-11i−iii−i−i1-111-1-1ii−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ111111-1-111-1-1-11-1111-1-1-1-1111-1-11-1-1-11111−i−iii1111-1-1-1-1-1-1−i−i−i−iiiii-11−ii−i−iii1-111-1-1−i−iii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ121111-1-111-1-1-11-1111-1-1-1-1111-1-11-1-1-11111−i−iii1111-1-1-1-1-1-1−i−i−i−iiiii-11−ii−i−iii1-111-1-1−i−iii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ131111-1-111-1-1-11-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1ii−i−i1111-1-11111iiii−i−i−i−i1-1i−i−i−iii1-1-1-111ii−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111-1-111-1-1-11-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1ii−i−i1111-1-11111iiii−i−i−i−i1-1i−i−i−iii1-1-1-111ii−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111-1-111-1-1-11-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1−i−iii1111-1-11111−i−i−i−iiiii1-1−iiii−i−i1-1-1-111−i−iiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111-1-111-1-1-11-1111-1-1-1-1-1-11111-1-1-1-1-1-1-1−i−iii1111-1-11111−i−i−i−iiiii1-1−iiii−i−i1-1-1-111−i−iiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ17222222222-222-2222222222-222-2-2222222000022-2-2-2-2222200000000-2-2000000-2-2-2-2-2-2000000000000000000000000
χ18222222222-222-22222222-2-2-2-2-2-2-222-2-2-2-2000022-2-2-2-2-2-2-2-20000000022000000-2-22222000000000000000000000000
χ192222222-2-22-2-22222-2-2-2-200200-2-22200000000-2-2-2-22200000000000000002i−2i2i−2i2-2000000002i2i−2i−2i2i2i−2i−2i000000000000
χ202222222-2-22-2-22222-2-2-2-200200-2-22200000000-2-2-2-2220000000000000000−2i2i−2i2i2-200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ212222222-2-2-2-2-2-2222-2-2-2-200-200222200002i2i−2i−2i-2-222-2-200002i2i2i2i−2i−2i−2i−2i00−2i2i0000-220000−2i−2i2i2i00000000000000000000
χ222222222-2-2-2-2-2-2222-2-2-2-200-20022220000−2i−2i2i2i-2-222-2-20000−2i−2i−2i−2i2i2i2i2i002i−2i0000-2200002i2i−2i−2i00000000000000000000
χ23222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ24222222-1222222-1-1-1-1-1-1-12222222-1-1-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-11111111122-2-2-2-2-2-2-1-1-1-1-1-1111111111111000000000000
χ25222222-1222222-1-1-1-1-1-1-1-2-22-2-222-1-111112222-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-222-2-2-2-2-1-11111-1-1-1-111111111000000000000
χ26222222-1222222-1-1-1-1-1-1-1-2-22-2-222-1-11111-2-2-2-2-1-1-1-1-1-1111111111111-2-2-2-22222-1-111111111-1-1-1-1-1-1-1-1000000000000
χ27222222-122-222-2-1-1-1-1-1-1-122-222-2-2-1-1-1-1-1-10000-1-11111-1-1-1-1−i3−i3i3i3−i3−i3i3i3-2-2000000111111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000
χ28222222-122-222-2-1-1-1-1-1-1-122-222-2-2-1-1-1-1-1-10000-1-11111-1-1-1-1i3i3−i3−i3i3i3−i3−i3-2-2000000111111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000
χ29222222-122-222-2-1-1-1-1-1-1-1-2-2-2-2-2-2-2-1-111110000-1-111111111−i3−i3i3i3−i3−i3i3i32200000011-1-1-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3000000000000
χ30222222-122-222-2-1-1-1-1-1-1-1-2-2-2-2-2-2-2-1-111110000-1-111111111i3i3−i3−i3i3i3−i3−i32200000011-1-1-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3000000000000
χ31222222-1-2-22-2-22-1-1-1111100200-2-2-1-1−i3−i3i3i300001111-1-1−i3−i3i3i333−3−3−3−33300002i−2i2i−2i-11−i3i3−i3i3−333−3−i−iii−i−iii000000000000
χ32222222-1-2-22-2-22-1-1-1111100200-2-2-1-1−i3−i3i3i300001111-1-1−i3−i3i3i3−3−33333−3−30000−2i2i−2i2i-11−i3i3−i3i33−3−33ii−i−iii−i−i000000000000
χ33222222-1-2-22-2-22-1-1-1111100200-2-2-1-1i3i3−i3−i300001111-1-1i3i3−i3−i333−3−3−3−3330000−2i2i−2i2i-11i3−i3i3−i3−333−3ii−i−iii−i−i000000000000
χ34222222-1-2-22-2-22-1-1-1111100200-2-2-1-1i3i3−i3−i300001111-1-1i3i3−i3−i3−3−33333−3−300002i−2i2i−2i-11i3−i3i3−i33−3−33−i−iii−i−iii000000000000
χ35222222-1-2-2-2-2-2-2-1-1-1111100-20022-1-1−i3−i3i3i32i2i−2i−2i11-1-111−i3−i3i3i3−i−i−i−iiiii00−2i2i00001-1i3−i3i3−i3ii−i−i3−3−333−3−33000000000000
χ36222222-1-2-2-2-2-2-2-1-1-1111100-20022-1-1−i3−i3i3i3−2i−2i2i2i11-1-111−i3−i3i3i3iiii−i−i−i−i002i−2i00001-1i3−i3i3−i3−i−iii−333−3−333−3000000000000
χ37222222-1-2-2-2-2-2-2-1-1-1111100-20022-1-1i3i3−i3−i32i2i−2i−2i11-1-111i3i3−i3−i3−i−i−i−iiiii00−2i2i00001-1−i3i3−i3i3ii−i−i−333−3−333−3000000000000
χ38222222-1-2-2-2-2-2-2-1-1-1111100-20022-1-1i3i3−i3−i3−2i−2i2i2i11-1-111i3i3−i3−i3iiii−i−i−i−i002i−2i00001-1−i3i3−i3i3−i−iii3−3−333−3−33000000000000
χ392222-2-222-22-222222-2-2-2-222-2-2-2-22-2-22222000022-2-222-2-2-2-2000000002-2000000-22-2-222000000000000000000000000
χ402222-2-222-22-222222-2-2-2-2-2-2-222-22-2-2-2-2-2-2000022-2-222222200000000-22000000-2222-2-2000000000000000000000000
χ412222-2-22-2222-22222222200-2002-2-2-200002222-2-2222200002222222200-2-20000-2-20000-2-2-2-200000000000000000000
χ422222-2-22-2222-22222222200-2002-2-2-20000-2-2-2-2-2-222220000-2-2-2-2-2-2-2-200220000-2-20000222200000000000000000000
χ432222-2-22-22-22-2-2222222200200-22-2-200000000-2-2-2-2-2-200000000000000002-2-22220000000022-2-2-2-222000000000000
χ442222-2-22-22-22-2-2222222200200-22-2-200000000-2-2-2-2-2-20000000000000000-222-22200000000-2-22222-2-2000000000000
χ452222-2-2-12-22-222-1-1-1111122-2-2-2-2211-1-1-1-10000-1-111-1-1111133−3−3−3−3332-20000001-111-1-13−3−333−33−3−33−33000000000000
χ462222-2-2-12-22-222-1-1-1111122-2-2-2-2211-1-1-1-10000-1-111-1-11111−3−33333−3−32-20000001-111-1-1−333−3−33−333−33−3000000000000
χ472222-2-2-12-22-222-1-1-11111-2-2-222-221111110000-1-111-1-1-1-1-1-133−3−3−3−333-220000001-1-1-1113−3−33−33−333−33−3000000000000
χ482222-2-2-12-22-222-1-1-11111-2-2-222-221111110000-1-111-1-1-1-1-1-1−3−33333−3−3-220000001-1-1-111−333−33−33−3−33−33000000000000
χ492222-2-2-12-2-2-22-2-1-1-11111222-2-22-211-1-1-1-12i2i−2i−2i-1-1-1-1111111−i−i−i−iiiii-222i−2i2i2i−2i−2i-11-1-111−i−iii−i−i−i−iiiii000000000000
χ502222-2-2-12-2-2-22-2-1-1-11111222-2-22-211-1-1-1-1−2i−2i2i2i-1-1-1-1111111iiii−i−i−i−i-22−2i2i−2i−2i2i2i-11-1-111ii−i−iiiii−i−i−i−i000000000000
χ512222-2-2-12-2-2-22-2-1-1-11111-2-22222-21111112i2i−2i−2i-1-1-1-111-1-1-1-1−i−i−i−iiiii2-22i−2i−2i−2i2i2i-1111-1-1−i−iiiiiii−i−i−i−i000000000000
χ522222-2-2-12-2-2-22-2-1-1-11111-2-22222-2111111−2i−2i2i2i-1-1-1-111-1-1-1-1iiii−i−i−i−i2-2−2i2i2i2i−2i−2i-1111-1-1ii−i−i−i−i−i−iiiii000000000000
χ532222-2-2-1-2222-22-1-1-1-1-1-1-100-2002-211−i3−i3i3i3222211-1-1-1-1i3i3−i3−i3-1-1-1-1-1-1-1-100-2-2000011i3−i3−i3i31111−i3i3i3−i3i3−i3−i3i3000000000000
χ542222-2-2-1-2222-22-1-1-1-1-1-1-100-2002-211−i3−i3i3i3-2-2-2-211-1-1-1-1i3i3−i3−i3111111110022000011i3−i3−i3i3-1-1-1-1i3−i3−i3i3−i3i3i3−i3000000000000
χ552222-2-2-1-2222-22-1-1-1-1-1-1-100-2002-211i3i3−i3−i3222211-1-1-1-1−i3−i3i3i3-1-1-1-1-1-1-1-100-2-2000011−i3i3i3−i31111i3−i3−i3i3−i3i3i3−i3000000000000
χ562222-2-2-1-2222-22-1-1-1-1-1-1-100-2002-211i3i3−i3−i3-2-2-2-211-1-1-1-1−i3−i3i3i3111111110022000011−i3i3i3−i3-1-1-1-1−i3i3i3−i3i3−i3−i3i3000000000000
χ572222-2-2-1-22-22-2-2-1-1-1-1-1-1-100200-2211−i3−i3i3i30000111111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300002-2-22-1-1−i3i3i3−i3i3−i3i3−i3-1-11111-1-1000000000000
χ582222-2-2-1-22-22-2-2-1-1-1-1-1-1-100200-2211−i3−i3i3i30000111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000-222-2-1-1−i3i3i3−i3−i3i3−i3i311-1-1-1-111000000000000
χ592222-2-2-1-22-22-2-2-1-1-1-1-1-1-100200-2211i3i3−i3−i30000111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000-222-2-1-1i3−i3−i3i3i3−i3i3−i311-1-1-1-111000000000000
χ602222-2-2-1-22-22-2-2-1-1-1-1-1-1-100200-2211i3i3−i3−i30000111111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300002-2-22-1-1i3−i3−i3i3−i3i3−i3i3-1-11111-1-1000000000000
χ6122-2-22-22220-2-202-2-222-2-22-202-2002-22-22-200002-200002-22-200000000000000000000000000000000002−22−22−22−20000
χ6222-2-22-22220-2-202-2-222-2-22-202-2002-22-22-200002-200002-22-20000000000000000000000000000000000−22−22−22−220000
χ6322-2-22-22220-2-202-2-222-2-2-220-22002-2-22-2200002-20000-22-2200000000000000000000000000000000002−22−2−22−220000
χ6422-2-22-22220-2-202-2-222-2-2-220-22002-2-22-2200002-20000-22-220000000000000000000000000000000000−22−222−22−20000
χ6522-2-2-2222-202-202-2-2-2-2222-20-2200-222-22-200002-20000-22-220000000000000000000000000000000000−i2i2i2−i2−i2i2i2−i20000
χ6622-2-2-2222-202-202-2-2-2-2222-20-2200-222-22-200002-20000-22-220000000000000000000000000000000000i2−i2−i2i2i2−i2−i2i20000
χ6722-2-2-2222-202-202-2-2-2-222-2202-200-22-22-2200002-200002-22-20000000000000000000000000000000000−i2i2i2−i2i2−i2−i2i20000
χ6822-2-2-2222-202-202-2-2-2-222-2202-200-22-22-2200002-200002-22-20000000000000000000000000000000000i2−i2−i2i2−i2i2i2−i20000
χ6944-4-44-44-4-404404-4-4-4-44400000004-400000000-44000000000000000000000000000000000000000000000000000000
χ7044-4-44-4-2440-4-40-222-2-2224-404-400-22-22-220000-220000-22-220000000000000000000000000000000000000000000000
χ7144-4-44-4-2440-4-40-222-2-222-440-4400-222-22-20000-2200002-22-20000000000000000000000000000000000000000000000
χ7244-4-44-4-2-4-40440-22222-2-20000000-22−2i32i32i3−2i300002-20000−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ7344-4-44-4-2-4-40440-22222-2-20000000-222i3−2i3−2i32i300002-200002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ7444-4-4-444-440-4404-4-444-4-40000000-4400000000-44000000000000000000000000000000000000000000000000000000
χ7544-4-4-44-24-404-40-22222-2-24-40-44002-2-22-220000-2200002-22-20000000000000000000000000000000000000000000000
χ7644-4-4-44-24-404-40-22222-2-2-4404-4002-22-22-20000-220000-22-220000000000000000000000000000000000000000000000
χ7744-4-4-44-2-440-440-222-2-22200000002-2−2i32i32i3−2i300002-200002i3−2i3−2i32i30000000000000000000000000000000000000000000000
χ7844-4-4-44-2-440-440-222-2-22200000002-22i3−2i3−2i32i300002-20000−2i32i32i3−2i30000000000000000000000000000000000000000000000
χ794-44-400400400-4-44-40000000000000000022−2222−2200004-4000022−2222−2222−2222−2200000000000000000000000000000000000000
χ804-44-400400400-4-44-400000000000000000−2222−222200004-40000−2222−2222−2222−222200000000000000000000000000000000000000
χ814-44-400400-4004-44-400000000000000000−2i22i22i2−2i20000-440000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000000000000000000000
χ824-44-400400-4004-44-4000000000000000002i2−2i2−2i22i20000-4400002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000000000000000000000
χ834-44-400-200400-42-2223−2323−23000000000000022−2222−220023−23-2200002ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ700000000000000000000000000000000000000
χ844-44-400-200400-42-2223−2323−230000000000000−2222−22220023−23-220000−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ23−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ700000000000000000000000000000000000000
χ854-44-400-200400-42-22−2323−2323000000000000022−2222−2200−2323-2200002ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ2300000000000000000000000000000000000000
χ864-44-400-200400-42-22−2323−23230000000000000−2222−222200−2323-220000−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ7−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ2300000000000000000000000000000000000000
χ874-44-400-200-40042-2223−2323−230000000000000−2i22i22i2−2i200−23232-200002ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ23−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ700000000000000000000000000000000000000
χ884-44-400-200-40042-2223−2323−2300000000000002i2−2i2−2i22i200−23232-20000−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ232ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ700000000000000000000000000000000000000
χ894-44-400-200-40042-22−2323−23230000000000000−2i22i22i2−2i20023−232-200002ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ7−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ2300000000000000000000000000000000000000
χ904-44-400-200-40042-22−2323−232300000000000002i2−2i2−2i22i20023−232-20000−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ72ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ2300000000000000000000000000000000000000
χ918-8-88008000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-8-8800-400000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000000000
χ938-8-8800-400000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000000000

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