Finite Group Databasebeta

← Group #10690147

Character table — Group #10690147

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11111111222222224444444444888888888888888888881616161616161616161624242424242424242424242424242424
order1222444436661212121224444466121222448888121212122424242424242424246666121212128888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ711111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-1111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-11111-1-1-1-1-1111-1-1-1-1111-11-111-1-111-1-11111-1-1-1-11-11-1111-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-11111-1-1-1-1-1111-1-1-1-1111-11-111-1-111-1-11111-1-1-1-11-11-1111-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1111-11-1-1-11111-1-1-1-1-1-11111-111-1-1-11-111ii−i−iii−i−i−i−iii−i−iii
χ121111-1-1-1-11111-1-1-1-1-1111-1-1-1-1111-11-1-1-11111-1-1-1-1-1-11111-111-1-1-11-111−i−iii−i−iiiii−i−iii−i−i
χ131111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-11-1111-1-111-1-11111-1-1-1-1-11-11-1-1-1111ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-11-1111-1-111-1-11111-1-1-1-1-11-11-1-1-1111−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-11-11-1-11111-1-1-1-1-1-111111-1-1111-11-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-11111-1-1-1-1-1111-1-1-1-111-11-11-1-11111-1-1-1-1-1-111111-1-1111-11-1-1−i−iiiii−i−iii−i−i−i−iii
χ1722222222222222222-2-22-2-222222-2-220000-2-2-2-200000000002-200-22000000000000000000
χ1822222222222222222-2-22-2-22222-222-20000-2-2-2-20000000000-22002-2000000000000000000
χ192222222222222222-22-2-22-2-2-2-2-2000000002-22-200000000000000000000002-22-200000000
χ202222222222222222-22-2-22-2-2-2-2-2000000002-22-20000000000000000000000-22-2200000000
χ212222222222222222-2-22-2-22-2-2-2-200000000-22-220000000000000000002-22-2000000000000
χ222222222222222222-2-22-2-22-2-2-2-200000000-22-22000000000000000000-22-22000000000000
χ2322222222-1-1-1-1-1-1-1-1222222-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-10000000000000000
χ2422222222-1-1-1-1-1-1-1-1222222-1-1-1-12222-2-2-2-2-1-1-1-111111111-2-2-1-111-1-1110000000000000000
χ2522222222-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-2-2111111110000000000000000
χ2622222222-1-1-1-1-1-1-1-1222222-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1111111112211-1-111-1-10000000000000000
χ2722222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-12-2-2200001111−i3−i3i3i3−i3−i3i3i300-11−i3i31-1−i3i30000000000000000
χ2822222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-12-2-2200001111i3i3−i3−i3i3i3−i3−i300-11i3−i31-1i3−i30000000000000000
χ2922222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-1-222-200001111−i3−i3i3i3−i3−i3i3i3001-1i3−i3-11i3−i30000000000000000
χ3022222222-1-1-1-1-1-1-1-12-2-22-2-2-1-1-1-1-222-200001111i3i3−i3−i3i3i3−i3−i3001-1−i3i3-11−i3i30000000000000000
χ312222-2-2-2-22222-2-2-2-222-2-2-2222-2-2000000002-2-2200000000000000000000002i−2i−2i2i00000000
χ322222-2-2-2-22222-2-2-2-222-2-2-2222-2-2000000002-2-220000000000000000000000−2i2i2i−2i00000000
χ332222-2-2-2-22222-2-2-2-22-22-22-222-2-200000000-222-20000000000000000002i−2i−2i2i000000000000
χ342222-2-2-2-22222-2-2-2-22-22-22-222-2-200000000-222-2000000000000000000−2i2i2i−2i000000000000
χ352222-2-2-2-22222-2-2-2-2-2-2-2222-2-22222-2-20000-2-22200000000002200-2-2000000000000000000
χ362222-2-2-2-22222-2-2-2-2-2-2-2222-2-222-2-2220000-2-2220000000000-2-20022000000000000000000
χ372222-2-2-2-2-1-1-1-11111-2222-2-211-1-12-22-222-2-2-1-111-1-1-1-111112-2-11-1-1-11110000000000000000
χ382222-2-2-2-2-1-1-1-11111-2222-2-211-1-12-22-2-2-222-1-1111111-1-1-1-1-22-1111-11-1-10000000000000000
χ392222-2-2-2-2-1-1-1-11111-2222-2-211-1-1-22-2222-2-2-1-111-1-1-1-11111-221-1111-1-1-10000000000000000
χ402222-2-2-2-2-1-1-1-11111-2222-2-211-1-1-22-22-2-222-1-1111111-1-1-1-12-21-1-1-11-1110000000000000000
χ412222-2-2-2-2-1-1-1-11111-2-2-222211-1-122-2-2000011-1-1−i3−i3i3i3i3i3−i3−i300-1-1−i3i311i3−i30000000000000000
χ422222-2-2-2-2-1-1-1-11111-2-2-222211-1-122-2-2000011-1-1i3i3−i3−i3−i3−i3i3i300-1-1i3−i311−i3i30000000000000000
χ432222-2-2-2-2-1-1-1-11111-2-2-222211-1-1-2-222000011-1-1−i3−i3i3i3i3i3−i3−i30011i3−i3-1-1−i3i30000000000000000
χ442222-2-2-2-2-1-1-1-11111-2-2-222211-1-1-2-222000011-1-1i3i3−i3−i3−i3−i3i3i30011−i3i3-1-1i3−i30000000000000000
χ4544444444-2-2-2-2-2-2-2-2-44-4-44-4222200000000-22-220000000000000000000000000000000000
χ4644444444-2-2-2-2-2-2-2-2-4-44-4-442222000000002-22-20000000000000000000000000000000000
χ474444-4-4-4-4-2-2-2-2222244-4-4-44-2-22200000000-222-20000000000000000000000000000000000
χ484444-4-4-4-4-2-2-2-222224-44-44-4-2-222000000002-2-220000000000000000000000000000000000
χ4944-4-44i4i−4i−4i44-4-44i4i−4i−4i0000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000
χ5044-4-44i4i−4i−4i44-4-44i4i−4i−4i000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000
χ5144-4-4−4i−4i4i4i44-4-4−4i−4i4i4i000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ5244-4-4−4i−4i4i4i44-4-4−4i−4i4i4i0000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ534-44-44i−4i4i−4i4-44-44i−4i4i−4i00000000000000000000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13
χ544-44-44i−4i4i−4i4-44-44i−4i4i−4i0000000000000000000000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13
χ554-44-4−4i4i−4i4i4-44-4−4i4i−4i4i0000000000000000000000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23
χ564-44-4−4i4i−4i4i4-44-4−4i4i−4i4i00000000000000000000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23
χ574-4-444-4-444-4-444-4-44000000000000002-22-200002-22-22-22-200000000000000000000000000
χ584-4-444-4-444-4-444-4-4400000000000000-22-220000-22-22-22-2200000000000000000000000000
χ594-4-444-4-44-222-2-222-2000000−2i32i3−2i32i300002-22-20000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i300000000000000000000000000
χ604-4-444-4-44-222-2-222-2000000−2i32i3−2i32i30000-22-2200001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i300000000000000000000000000
χ614-4-444-4-44-222-2-222-20000002i3−2i32i3−2i300002-22-20000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i300000000000000000000000000
χ624-4-444-4-44-222-2-222-20000002i3−2i32i3−2i30000-22-2200001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i300000000000000000000000000
χ634-4-44-444-44-4-44-444-4000000000000002-2-2200002-22-2-22-2200000000000000000000000000
χ644-4-44-444-44-4-44-444-400000000000000-222-20000-22-222-22-200000000000000000000000000
χ654-4-44-444-4-222-22-2-22000000−2i32i32i3−2i300002-2-220000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000000000
χ664-4-44-444-4-222-22-2-22000000−2i32i32i3−2i30000-222-200001−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000000000
χ674-4-44-444-4-222-22-2-220000002i3−2i3−2i32i300002-2-220000−1−i31+i3−1+i31−i31+i3−1−i31−i3−1+i300000000000000000000000000
χ684-4-44-444-4-222-22-2-220000002i3−2i3−2i32i30000-222-200001+i3−1−i31−i3−1+i3−1−i31+i3−1+i31−i300000000000000000000000000
χ6988-8-88i8i−8i−8i-4-444−4i−4i4i4i00000000000000000000000000000000000000000000000000000000
χ7088-8-8−8i−8i8i8i-4-4444i4i−4i−4i00000000000000000000000000000000000000000000000000000000
χ718-88-88i−8i8i−8i-44-44−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ728-88-8−8i8i−8i8i-44-444i−4i4i−4i00000000000000000000000000000000000000000000000000000000

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