Finite Group Databasebeta

← Group #10690138

Character table — Group #10690138

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111222222224444444444888888888888888888881616161616161616161624242424242424242424242424242424
order122244443666121212122444441212121268888888812121224242424242424244412121212242424244444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-11111-1-1-1-1-111-11-111-1-1-1ii−i−iii−i−i11-1iiii−i−i−i−i1-111-1-1ii−i−i11-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-11111-1-1-1-1-111-11-111-1-1-1ii−i−iii−i−i11-1iiii−i−i−i−i1-111-1-1ii−i−i-1-111−i−iii−i−iii-1-111
χ111111-1-1-1-11111-1-1-1-1-111-11-111-1-1-1ii−i−i−i−iii11-1−i−i−i−iiiii-11-1-111ii−i−i11-1-1ii−i−i−i−iii-1-111
χ121111-1-1-1-11111-1-1-1-1-111-11-111-1-1-1ii−i−i−i−iii11-1−i−i−i−iiiii-11-1-111ii−i−i-1-111−i−iiiii−i−i11-1-1
χ131111-1-1-1-11111-1-1-1-1-111-11-111-1-1-1−i−iiiii−i−i11-1iiii−i−i−i−i-11-1-111−i−iii11-1-1−i−iiiii−i−i-1-111
χ141111-1-1-1-11111-1-1-1-1-111-11-111-1-1-1−i−iiiii−i−i11-1iiii−i−i−i−i-11-1-111−i−iii-1-111ii−i−i−i−iii11-1-1
χ151111-1-1-1-11111-1-1-1-1-111-11-111-1-1-1−i−iii−i−iii11-1−i−i−i−iiiii1-111-1-1−i−iii11-1-1−i−iii−i−iii11-1-1
χ161111-1-1-1-11111-1-1-1-1-111-11-111-1-1-1−i−iii−i−iii11-1−i−i−i−iiiii1-111-1-1−i−iii-1-111ii−i−iii−i−i-1-111
χ1722222222222222222-2-2-22-2-2-2-2-22000000002-2-20000000000000000002-22-2000000000000
χ1822222222222222222-2-2-22-2-2-2-2-22000000002-2-2000000000000000000-22-22000000000000
χ192222222222222222-22-22-2-22222-22-22-20000-2-2-2000000000000002-22-20000000000000000
χ202222222222222222-22-22-2-22222-2-22-220000-2-2-200000000000000-22-220000000000000000
χ212222222222222222-2-22-2-22-2-2-2-2-200000000-22200000000000000000000002-22-200000000
χ222222222222222222-2-22-2-22-2-2-2-2-200000000-2220000000000000000000000-22-2200000000
χ2322222222-1-1-1-1-1-1-1-1222222-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000000000000
χ2422222222-1-1-1-1-1-1-1-1222222-1-1-1-1-12222-2-2-2-2-1-1-111111111-2-21111-1-1-1-10000000000000000
χ2522222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-2-2111111110000000000000000
χ2622222222-1-1-1-1-1-1-1-1222222-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-11111111122-1-1-1-111110000000000000000
χ2722222222-1-1-1-1-1-1-1-1-22-22-2-2-1-1-1-112-22-20000111−i3−i3i3i3−i3−i3i3i300−i3i3−i3i3-11-110000000000000000
χ2822222222-1-1-1-1-1-1-1-1-22-22-2-2-1-1-1-112-22-20000111i3i3−i3−i3i3i3−i3−i300i3−i3i3−i3-11-110000000000000000
χ2922222222-1-1-1-1-1-1-1-1-22-22-2-2-1-1-1-11-22-220000111−i3−i3i3i3−i3−i3i3i300i3−i3i3−i31-11-10000000000000000
χ3022222222-1-1-1-1-1-1-1-1-22-22-2-2-1-1-1-11-22-220000111i3i3−i3−i3i3i3−i3−i300−i3i3−i3i31-11-10000000000000000
χ312222-2-2-2-22222-2-2-2-222-2-2-2222-2-222i−2i−2i2i0000-2-22000000000000002i−2i−2i2i0000000000000000
χ322222-2-2-2-22222-2-2-2-222-2-2-2222-2-22−2i2i2i−2i0000-2-2200000000000000−2i2i2i−2i0000000000000000
χ332222-2-2-2-22222-2-2-2-22-222-2-2-2-222200000000-22-200000000000000000000002i−2i−2i2i00000000
χ342222-2-2-2-22222-2-2-2-22-222-2-2-2-222200000000-22-20000000000000000000000−2i2i2i−2i00000000
χ352222-2-2-2-22222-2-2-2-2-2-2-2222-2-222-2000000002-220000000000000000002-2-22000000000000
χ362222-2-2-2-22222-2-2-2-2-2-2-2222-2-222-2000000002-22000000000000000000-222-2000000000000
χ372222-2-2-2-2-1-1-1-1111122-2-2-22-1-111-12i−2i−2i2i000011-133−3−3−3−33300−i3i3i3−i3−iii−i0000000000000000
χ382222-2-2-2-2-1-1-1-1111122-2-2-22-1-111-12i−2i−2i2i000011-1−3−33333−3−300i3−i3−i3i3−iii−i0000000000000000
χ392222-2-2-2-2-1-1-1-1111122-2-2-22-1-111-1−2i2i2i−2i000011-133−3−3−3−33300i3−i3−i3i3i−i−ii0000000000000000
χ402222-2-2-2-2-1-1-1-1111122-2-2-22-1-111-1−2i2i2i−2i000011-1−3−33333−3−300−i3i3i3−i3i−i−ii0000000000000000
χ412222-2-2-2-2-1-1-1-11111-222-22-2-1-11112i2i−2i−2i2i2i−2i−2i-1-11−i−i−i−iiiii2-2-1-111−i−iii0000000000000000
χ422222-2-2-2-2-1-1-1-11111-222-22-2-1-11112i2i−2i−2i−2i−2i2i2i-1-11iiii−i−i−i−i-2211-1-1−i−iii0000000000000000
χ432222-2-2-2-2-1-1-1-11111-222-22-2-1-1111−2i−2i2i2i2i2i−2i−2i-1-11−i−i−i−iiiii-2211-1-1ii−i−i0000000000000000
χ442222-2-2-2-2-1-1-1-11111-222-22-2-1-1111−2i−2i2i2i−2i−2i2i2i-1-11iiii−i−i−i−i2-2-1-111ii−i−i0000000000000000
χ4544444444-2-2-2-2-2-2-2-24-4-4-44-42222-200000000-2220000000000000000000000000000000000
χ4644444444-2-2-2-2-2-2-2-2-4-44-4-4422222000000002-2-20000000000000000000000000000000000
χ474444-4-4-4-4-2-2-2-222224-444-4-422-2-2-2000000002-220000000000000000000000000000000000
χ484444-4-4-4-4-2-2-2-22222-4-4-444422-2-2200000000-22-20000000000000000000000000000000000
χ4944-4-444-4-444-4-444-4-400000000000000000000000000000000000000000000000000002-22-2
χ5044-4-444-4-444-4-444-4-40000000000000000000000000000000000000000000000000000-22-22
χ5144-4-4-4-44444-4-4-4-44400000000000000000000000000000000000000000000000000002-2-22
χ5244-4-4-4-44444-4-4-4-4440000000000000000000000000000000000000000000000000000-222-2
χ534-44-44i−4i4i−4i4-44-44i−4i4i−4i0000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000
χ544-44-44i−4i4i−4i4-44-44i−4i4i−4i000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000
χ554-44-44i−4i4i−4i-22-22−2i2i−2i2i000000−2i32i323−23000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000−2ζ72ζ7−2ζ232ζ232ζ13−2ζ132ζ5−2ζ500000000000000000000000000
χ564-44-44i−4i4i−4i-22-22−2i2i−2i2i000000−2i32i323−2300000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130002ζ7−2ζ72ζ23−2ζ23−2ζ132ζ13−2ζ52ζ500000000000000000000000000
χ574-44-44i−4i4i−4i-22-22−2i2i−2i2i0000002i3−2i3−2323000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000−2ζ232ζ23−2ζ72ζ72ζ5−2ζ52ζ13−2ζ1300000000000000000000000000
χ584-44-44i−4i4i−4i-22-22−2i2i−2i2i0000002i3−2i3−232300000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130002ζ23−2ζ232ζ7−2ζ7−2ζ52ζ5−2ζ132ζ1300000000000000000000000000
χ594-44-4−4i4i−4i4i4-44-4−4i4i−4i4i000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000
χ604-44-4−4i4i−4i4i4-44-4−4i4i−4i4i0000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000
χ614-44-4−4i4i−4i4i-22-222i−2i2i−2i000000−2i32i3−232300000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230002ζ13−2ζ132ζ5−2ζ5−2ζ72ζ7−2ζ232ζ2300000000000000000000000000
χ624-44-4−4i4i−4i4i-22-222i−2i2i−2i000000−2i32i3−2323000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000−2ζ132ζ13−2ζ52ζ52ζ7−2ζ72ζ23−2ζ2300000000000000000000000000
χ634-44-4−4i4i−4i4i-22-222i−2i2i−2i0000002i3−2i323−2300000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230002ζ5−2ζ52ζ13−2ζ13−2ζ232ζ23−2ζ72ζ700000000000000000000000000
χ644-44-4−4i4i−4i4i-22-222i−2i2i−2i0000002i3−2i323−23000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000−2ζ52ζ5−2ζ132ζ132ζ23−2ζ232ζ7−2ζ700000000000000000000000000
χ654-4-444i−4i−4i4i4-4-444i−4i−4i4i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ664-4-444i−4i−4i4i4-4-444i−4i−4i4i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ674-4-44−4i4i4i−4i4-4-44−4i4i4i−4i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ684-4-44−4i4i4i−4i4-4-44−4i4i4i−4i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ6988-8-888-8-8-4-444-4-44400000000000000000000000000000000000000000000000000000000
χ7088-8-8-8-888-4-44444-4-400000000000000000000000000000000000000000000000000000000
χ718-8-888i−8i−8i8i-444-4−4i4i4i−4i00000000000000000000000000000000000000000000000000000000
χ728-8-88−8i8i8i−8i-444-44i−4i−4i4i00000000000000000000000000000000000000000000000000000000

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