Finite Group Databasebeta

← Group #10692288

Character table — Group #10692288

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444444448888888888888888881212121212121212161616161616161616162424242448484848
order12223444444666244466121212121212121288888888121224242424242424244444888844121212122424242424888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ51111111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111
χ81111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-11111-1-1
χ9111111-1-1-1-1111111-1-11111-1-1-1-1-1-1ii−i−iii−i−i1-1iiii−i−i−i−i11-1-1ii−i−i1-111-1-1ii−i−i1-1i−ii−i1-1
χ10111111-1-1-1-1111111-1-11111-1-1-1-1-1-1ii−i−iii−i−i1-1iiii−i−i−i−i-1-111−i−iii1-111-1-1ii−i−i-11−ii−ii-11
χ11111111-1-1-1-1111111-1-11111-1-1-1-1-1-1ii−i−i−i−iii1-1−i−i−i−iiiii11-1-1ii−i−i-11-1-111ii−i−i1-1i−i−ii-11
χ12111111-1-1-1-1111111-1-11111-1-1-1-1-1-1ii−i−i−i−iii1-1−i−i−i−iiiii-1-111−i−iii-11-1-111ii−i−i-11−iii−i1-1
χ13111111-1-1-1-1111111-1-11111-1-1-1-1-1-1−i−iiiii−i−i1-1iiii−i−i−i−i11-1-1−i−iii-11-1-111−i−iii1-1−iii−i-11
χ14111111-1-1-1-1111111-1-11111-1-1-1-1-1-1−i−iiiii−i−i1-1iiii−i−i−i−i-1-111ii−i−i-11-1-111−i−iii-11i−i−ii1-1
χ15111111-1-1-1-1111111-1-11111-1-1-1-1-1-1−i−iii−i−iii1-1−i−i−i−iiiii11-1-1−i−iii1-111-1-1−i−iii1-1−ii−ii1-1
χ16111111-1-1-1-1111111-1-11111-1-1-1-1-1-1−i−iii−i−iii1-1−i−i−i−iiiii-1-111ii−i−i1-111-1-1−i−iii-11i−ii−i-11
χ1722222222-2-22222-2-2-22-2-2222222-2-200000000-2-20000000022-2-200000000000000-22000000
χ1822222222-2-22222-2-2-22-2-2222222-2-200000000-2-200000000-2-222000000000000002-2000000
χ19222222-2-2222222-2-22-2-2-222-2-2-2-22200000000-2200000000222200000000000000-2-2000000
χ20222222-2-2222222-2-22-2-2-222-2-2-2-22200000000-2200000000-2-2-2-20000000000000022000000
χ2122222-22222-2222-22-2-2-2-2-2-222-2-222000000002-20000000000002222000000000000-2-20000
χ2222222-22222-2222-22-2-2-2-2-2-222-2-222000000002-2000000000000-2-2-2-2000000000000220000
χ2322222-222-2-2-22222-22-222-2-222-2-2-2-22i−2i2i−2i0000-2200000000000000000000002i−2i2i−2i00000000
χ2422222-222-2-2-22222-22-222-2-222-2-2-2-2−2i2i−2i2i0000-220000000000000000000000−2i2i−2i2i00000000
χ2522222-2-2-222-22222-2-2222-2-2-2-222222-2-220000-2-200000000000000000000002-2-2200000000
χ2622222-2-2-222-22222-2-2222-2-2-2-22222-222-20000-2-20000000000000000000000-222-200000000
χ2722222-2-2-2-2-2-2222-2222-2-2-2-2-2-222-2-200000000220000000000002i2i−2i−2i000000000000−2i2i0000
χ2822222-2-2-2-2-2-2222-2222-2-2-2-2-2-222-2-20000000022000000000000−2i−2i2i2i0000000000002i−2i0000
χ292222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-10000000022-1-1-1-1-1-1-1-100000000
χ302222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-12222-2-2-2-2-1-11111111100000000-2-21111-1-1-1-100000000
χ312222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-22222-1-1-1-1-1-1-1-1-1-100000000-2-21111111100000000
χ322222-1222222-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1111111110000000022-1-1-1-1111100000000
χ332222-12-2-2-2-22-1-1-122-2-2-1-1-1-11111112i2i−2i−2i2i2i−2i−2i-11−i−i−i−iiiii000000002-2-1-111−i−iii00000000
χ342222-12-2-2-2-22-1-1-122-2-2-1-1-1-11111112i2i−2i−2i−2i−2i2i2i-11iiii−i−i−i−i00000000-2211-1-1−i−iii00000000
χ352222-12-2-2-2-22-1-1-122-2-2-1-1-1-1111111−2i−2i2i2i2i2i−2i−2i-11−i−i−i−iiiii00000000-2211-1-1ii−i−i00000000
χ362222-12-2-2-2-22-1-1-122-2-2-1-1-1-1111111−2i−2i2i2i−2i−2i2i2i-11iiii−i−i−i−i000000002-2-1-111ii−i−i00000000
χ372222-1-222-2-2-2-1-1-12-22-2-1-111-1-111112i−2i2i−2i00001-133−3−333−3−30000000000−i3i3−i3i3−ii−ii00000000
χ382222-1-222-2-2-2-1-1-12-22-2-1-111-1-111112i−2i2i−2i00001-1−3−333−3−3330000000000i3−i3i3−i3−ii−ii00000000
χ392222-1-222-2-2-2-1-1-12-22-2-1-111-1-11111−2i2i−2i2i00001-133−3−333−3−30000000000i3−i3i3−i3i−ii−i00000000
χ402222-1-222-2-2-2-1-1-12-22-2-1-111-1-11111−2i2i−2i2i00001-1−3−333−3−3330000000000−i3i3−i3i3i−ii−i00000000
χ412222-1-2-2-222-2-1-1-12-2-22-1-11111-1-1-1-12-2-22000011−i3−i3i3i3i3i3−i3−i30000000000−i3i3i3−i3-111-100000000
χ422222-1-2-2-222-2-1-1-12-2-22-1-11111-1-1-1-12-2-22000011i3i3−i3−i3−i3−i3i3i30000000000i3−i3−i3i3-111-100000000
χ432222-1-2-2-222-2-1-1-12-2-22-1-11111-1-1-1-1-222-2000011−i3−i3i3i3i3i3−i3−i30000000000i3−i3−i3i31-1-1100000000
χ442222-1-2-2-222-2-1-1-12-2-22-1-11111-1-1-1-1-222-2000011i3i3−i3−i3−i3−i3i3i30000000000−i3i3i3−i31-1-1100000000
χ454444-2444-4-44-2-2-2-4-4-4422-2-2-2-2-2-22200000000220000000000000000000000000000000000
χ464444-24-4-4444-2-2-2-4-44-422-2-22222-2-2000000002-20000000000000000000000000000000000
χ474444-2-44444-4-2-2-2-44-4-42222-2-222-2-200000000-220000000000000000000000000000000000
χ484444-2-4-4-4-4-4-4-2-2-2-4444222222-2-22200000000-2-20000000000000000000000000000000000
χ4944-4-4440000-44-4-40000004-40000000000000000000000004-4000000000000000000000000
χ5044-4-4440000-44-4-40000004-4000000000000000000000000-44000000000000000000000000
χ5144-4-44-4000044-4-4000000-44000000000000000000000000004i−4i0000000000000000000000
χ5244-4-44-4000044-4-4000000-4400000000000000000000000000−4i4i0000000000000000000000
χ534-44-440004i−4i0-44-40000000000004i−4i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000
χ544-44-440004i−4i0-44-40000000000004i−4i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000
χ554-44-44000−4i4i0-44-4000000000000−4i4i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000
χ564-44-44000−4i4i0-44-4000000000000−4i4i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000
χ574-44-4-20004i−4i02-220000−2i32i3000023−23−2i2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ72ζ7−2ζ232ζ232ζ5−2ζ52ζ13−2ζ1300000000000000000000000000
χ584-44-4-20004i−4i02-220000−2i32i3000023−23−2i2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ7−2ζ72ζ23−2ζ23−2ζ52ζ5−2ζ132ζ1300000000000000000000000000
χ594-44-4-20004i−4i02-2200002i3−2i30000−2323−2i2i00002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300−2ζ232ζ23−2ζ72ζ72ζ13−2ζ132ζ5−2ζ500000000000000000000000000
χ604-44-4-20004i−4i02-2200002i3−2i30000−2323−2i2i0000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13002ζ23−2ζ232ζ7−2ζ7−2ζ132ζ13−2ζ52ζ500000000000000000000000000
χ614-44-4-2000−4i4i02-220000−2i32i30000−23232i−2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ13−2ζ132ζ5−2ζ5−2ζ232ζ23−2ζ72ζ700000000000000000000000000
χ624-44-4-2000−4i4i02-220000−2i32i30000−23232i−2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ132ζ13−2ζ52ζ52ζ23−2ζ232ζ7−2ζ700000000000000000000000000
χ634-44-4-2000−4i4i02-2200002i3−2i3000023−232i−2i0000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23002ζ5−2ζ52ζ13−2ζ13−2ζ72ζ7−2ζ232ζ2300000000000000000000000000
χ644-44-4-2000−4i4i02-2200002i3−2i3000023−232i−2i00002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300−2ζ52ζ5−2ζ132ζ132ζ7−2ζ72ζ23−2ζ2300000000000000000000000000
χ654-4-44404i−4i000-4-44000000004i−4i000000000000000000000000002+2i−2−2i2−2i−2+2i000000000000000000
χ664-4-44404i−4i000-4-44000000004i−4i00000000000000000000000000−2−2i2+2i−2+2i2−2i000000000000000000
χ674-4-4440−4i4i000-4-4400000000−4i4i000000000000000000000000002−2i−2+2i2+2i−2−2i000000000000000000
χ684-4-4440−4i4i000-4-4400000000−4i4i00000000000000000000000000−2+2i2−2i−2−2i2+2i000000000000000000
χ6988-8-8-480000-8-444000000-4400000000000000000000000000000000000000000000000000
χ7088-8-8-4-800008-4440000004-400000000000000000000000000000000000000000000000000
χ718-8-88-408i−8i00044-400000000−4i4i000000000000000000000000000000000000000000000000
χ728-8-88-40−8i8i00044-4000000004i−4i000000000000000000000000000000000000000000000000

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