Finite Group Databasebeta

← Group #10692014

Character table — Group #10692014

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12223444444446662441212121212121212121224446661212121212121224668812122424242488888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1
χ811111111111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ91111111-1-1-1-1-1-1111-111-1-1-1-111-1-1111-1-11-1111-1-1-1-1111-1111-1-1-111-1-1ii−i−iii−i−iii−i−ii−i
χ101111111-1-1-1-1-1-1111-111-1-1-1-111-1-1111-1-11-1111-1-1-1-1111-1111-1-1-111-1-1−i−iii−i−iii−i−iii−ii
χ111111111-1-1-1-1-1-1111-111-1-1-1-111-1-1111-1-11-1111-1-1-1-111-11-1-1-1111-1-111ii−i−i−i−iii−i−iiii−i
χ121111111-1-1-1-1-1-1111-111-1-1-1-111-1-1111-1-11-1111-1-1-1-111-11-1-1-1111-1-111−i−iiiii−i−iii−i−i−ii
χ131111111-1-1-1-1-1-1111-111-1-1-1-111-1-111-111-1-1-1-111111-1-11-111-11-1-1-1-111ii−i−iii−i−i−i−iii−ii
χ141111111-1-1-1-1-1-1111-111-1-1-1-111-1-111-111-1-1-1-111111-1-11-111-11-1-1-1-111−i−iii−i−iiiii−i−ii−i
χ151111111-1-1-1-1-1-1111-111-1-1-1-111-1-111-111-1-1-1-111111-1-1-11-1-11-11111-1-1ii−i−i−i−iiiii−i−i−ii
χ161111111-1-1-1-1-1-1111-111-1-1-1-111-1-111-111-1-1-1-111111-1-1-11-1-11-11111-1-1−i−iiiii−i−i−i−iiii−i
χ1722222222222-2-2222-2-2-222-2-2-2-2222222-2-2-222-222-2-2-2-200000000000000000000000000
χ1822222222222-2-2222-2-2-222-2-2-2-22222-2-222-2-2-2-2-2-2222200000000000000000000000000
χ192222222-2-2-2-2222222-2-2-2-222-2-2-2-2222-22-2222-2-2-222-2-200000000000000000000000000
χ202222222-2-2-2-2222222-2-2-2-222-2-2-2-222-22-222-2-2-222-2-22200000000000000000000000000
χ2122222-2-222-2-222222-2-22222222-2-2-2-20000-200-2000000000000000000000000002-22-200
χ2222222-2-222-2-222222-2-22222222-2-2-2-20000-200-200000000000000000000000000-22-2200
χ2322222-2-222-2-2-2-222222-222-2-2-2-2-2-2-2-20000200200000000000000000000002i−2i2i−2i000000
χ2422222-2-222-2-2-2-222222-222-2-2-2-2-2-2-2-2000020020000000000000000000000−2i2i−2i2i000000
χ2522222-2-2-2-22222222-22-2-2-222-2-222-2-20000-200200000000000000000000002-2-22000000
χ2622222-2-2-2-22222222-22-2-2-222-2-222-2-20000-20020000000000000000000000-222-2000000
χ2722222-2-2-2-222-2-22222-22-2-2-2-22222-2-20000200-2000000000000000000000000002i−2i−2i2i00
χ2822222-2-2-2-222-2-22222-22-2-2-2-22222-2-20000200-200000000000000000000000000−2i2i2i−2i00
χ292222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100000000000000
χ302222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-211111100000000000000
χ312222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-111-111111122-1-1-2-2-1-1111100000000000000
χ322222-122222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-111-1111111-2-2112211-1-1-1-100000000000000
χ332222-1222222-2-2-1-1-1-2-2-2-1-11111-1-1-1-122-2-21-1-11-1-1111100−i3i300−i3i3−i3i3−i3i300000000000000
χ342222-1222222-2-2-1-1-1-2-2-2-1-11111-1-1-1-122-2-21-1-11-1-1111100i3−i300i3−i3i3−i3i3−i300000000000000
χ352222-1222222-2-2-1-1-1-2-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-100−i3i300−i3i3i3−i3i3−i300000000000000
χ362222-1222222-2-2-1-1-1-2-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-100i3−i300i3−i3−i3i3−i3i300000000000000
χ372222-122-2-2-2-222-1-1-12-2-211-1-11111-1-12-22-2-1-1-1111-1-11100−i3i300i3−i3−i3i3i3−i300000000000000
χ382222-122-2-2-2-222-1-1-12-2-211-1-11111-1-12-22-2-1-1-1111-1-11100i3−i300−i3i3i3−i3−i3i300000000000000
χ392222-122-2-2-2-222-1-1-12-2-211-1-11111-1-1-22-22-1111-1-111-1-100−i3i300i3−i3i3−i3−i3i300000000000000
χ402222-122-2-2-2-222-1-1-12-2-211-1-11111-1-1-22-22-1111-1-111-1-100i3−i300−i3i3−i3i3i3−i300000000000000
χ412222-122-2-2-2-2-2-2-1-1-1-2221111-1-111-1-12-2-221-1-1-11111-1-12-2-1-12-211-1-11100000000000000
χ422222-122-2-2-2-2-2-2-1-1-1-2221111-1-111-1-12-2-221-1-1-11111-1-1-2211-22-1-111-1-100000000000000
χ432222-122-2-2-2-2-2-2-1-1-1-2221111-1-111-1-1-222-2111-1-1-1-1-1112-2-1-1-221111-1-100000000000000
χ442222-122-2-2-2-2-2-2-1-1-1-2221111-1-111-1-1-222-2111-1-1-1-1-111-22112-2-1-1-1-11100000000000000
χ454444-2-4-444-4-444-2-2-2-4-44-2-2-2-2-2-222220000200200000000000000000000000000000000
χ464444-2-4-444-4-4-4-4-2-2-244-4-2-2222222220000-200-200000000000000000000000000000000
χ474444-2-4-4-4-44444-2-2-2-44-422-2-222-2-2220000200-200000000000000000000000000000000
χ484444-2-4-4-4-444-4-4-2-2-24-442222-2-2-2-2220000-200200000000000000000000000000000000
χ4944-4-440000004i−4i4-4-4000004i−4i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000
χ5044-4-440000004i−4i4-4-4000004i−4i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000
χ5144-4-44000000−4i4i4-4-400000−4i4i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000
χ5244-4-44000000−4i4i4-4-400000−4i4i000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000
χ534-44-444-44i−4i4i−4i00-44-40004i−4i00004i−4i4-40000000000000000000000000000000000000000
χ544-44-444-4−4i4i−4i4i00-44-4000−4i4i0000−4i4i4-40000000000000000000000000000000000000000
χ554-44-44-444i−4i−4i4i00-44-40004i−4i0000−4i4i-440000000000000000000000000000000000000000
χ564-44-44-44−4i4i4i−4i00-44-4000−4i4i00004i−4i-440000000000000000000000000000000000000000
χ574-44-4-24-44i−4i4i−4i002-22000−2i2i0000−2i2i-2200000−2i32i3023−23000000000000000000000000000000
χ584-44-4-24-44i−4i4i−4i002-22000−2i2i0000−2i2i-22000002i3−2i30−2323000000000000000000000000000000
χ594-44-4-24-4−4i4i−4i4i002-220002i−2i00002i−2i-2200000−2i32i30−2323000000000000000000000000000000
χ604-44-4-24-4−4i4i−4i4i002-220002i−2i00002i−2i-22000002i3−2i3023−23000000000000000000000000000000
χ614-44-4-2-444i−4i−4i4i002-22000−2i2i00002i−2i2-20000000000−2i32i323−2300000000000000000000000000
χ624-44-4-2-444i−4i−4i4i002-22000−2i2i00002i−2i2-200000000002i3−2i3−232300000000000000000000000000
χ634-44-4-2-44−4i4i4i−4i002-220002i−2i0000−2i2i2-20000000000−2i32i3−232300000000000000000000000000
χ644-44-4-2-44−4i4i4i−4i002-220002i−2i0000−2i2i2-200000000002i3−2i323−2300000000000000000000000000
χ6588-8-8-40000008i−8i-44400000−4i4i0000000000000000000000000000000000000000000000
χ6688-8-8-4000000−8i8i-444000004i−4i0000000000000000000000000000000000000000000000
χ678-8-88800000000-8-8800000000000000000000000000000000000000000000000000000
χ688-8-88-40000000044-40000000−4i34i300000000000000000000000000000000000000000000
χ698-8-88-40000000044-400000004i3−4i300000000000000000000000000000000000000000000

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