Finite Group Databasebeta

← Group #10691972

Character table — Group #10691972

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order1222223444444666444661212121212121212224466661212121212124488121212122424242488888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1
χ91111-1-111-11-1-1-11111-11-1-11-1-111-1-111-11-111-1-11-111-1-11-11-111-1-111-1-1ii−i−iii−i−iii−i−ii−i
χ101111-1-111-11-1-1-11111-11-1-11-1-111-1-111-11-111-1-11-111-1-11-11-111-1-111-1-1−i−iii−i−iii−i−iii−ii
χ111111-1-111-11-1-1-11111-11-1-11-1-111-1-111-11-111-1-11-111-1-1-11-11-1-111-1-111ii−i−iii−i−i−i−iii−ii
χ121111-1-111-11-1-1-11111-11-1-11-1-111-1-111-11-111-1-11-111-1-1-11-11-1-111-1-111−i−iii−i−iiiii−i−ii−i
χ131111-1-111-11-1-1-11111-11-1-11-1-111-1-11-11-11-1-1111-1-1-1111-1-1111-1-1-1-111ii−i−i−i−iiiii−i−i−ii
χ141111-1-111-11-1-1-11111-11-1-11-1-111-1-11-11-11-1-1111-1-1-1111-1-1111-1-1-1-111−i−iiiii−i−i−i−iiii−i
χ151111-1-111-11-1-1-11111-11-1-11-1-111-1-11-11-11-1-1111-1-1-111-111-1-1-11111-1-1ii−i−i−i−iii−i−iiii−i
χ161111-1-111-11-1-1-11111-11-1-11-1-111-1-11-11-11-1-1111-1-1-111-111-1-1-11111-1-1−i−iiiii−i−iii−i−i−ii
χ1722222222222-2-2222-2-2-222222-2-2-2-2222-2-22222-2-2-2-2-2-200000000000000000000000000
χ1822222222222-2-2222-2-2-222222-2-2-2-22-2-222-2-2-2-2-2-2222200000000000000000000000000
χ192222222-2-2-2-222222-2-2222-2-2-22222-200000000-2-2000000000000000000002-22-2000000
χ202222222-2-2-2-222222-2-2222-2-2-22222-200000000-2-200000000000000000000-22-22000000
χ212222222-2-2-2-2-2-222222-222-2-2-2-2-2-2-2-2000000002200000000000000002i−2i2i−2i0000000000
χ222222222-2-2-2-2-2-222222-222-2-2-2-2-2-2-2-200000000220000000000000000−2i2i−2i2i0000000000
χ23222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ24222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ25222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111122-2-2-1-1-1-1111100000000000000
χ26222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-11111-2-2221111-1-1-1-100000000000000
χ27222222-12222-2-2-1-1-1-2-2-2-1-1-1-1-11111-122-2-2-1-1-1-11111110000−i3i3−i3i3−i3i3−i3i300000000000000
χ28222222-12222-2-2-1-1-1-2-2-2-1-1-1-1-11111-122-2-2-1-1-1-11111110000i3−i3i3−i3i3−i3i3−i300000000000000
χ29222222-12222-2-2-1-1-1-2-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-10000−i3i3−i3i3i3−i3i3−i300000000000000
χ30222222-12222-2-2-1-1-1-2-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-10000i3−i3i3−i3−i3i3−i3i300000000000000
χ312222-2-222-22-222222-22-2-2-22-2-2-2-22222-2-2222-2-2-22-2-22200000000000000000000000000
χ322222-2-222-22-222222-22-2-2-22-2-2-2-2222-222-2-2-222-2222-2-200000000000000000000000000
χ332222-2-22-22-22222222-2-2-2-2-222-2-222-2000000002-200000000000000002-2-220000000000
χ342222-2-22-22-22222222-2-2-2-2-222-2-222-2000000002-20000000000000000-222-20000000000
χ352222-2-22-22-22-2-2222-222-2-2-22222-2-2-200000000-22000000000000000000002i−2i−2i2i000000
χ362222-2-22-22-22-2-2222-222-2-2-22222-2-2-200000000-2200000000000000000000−2i2i2i−2i000000
χ372222-2-2-12-22-222-1-1-1-22-211-11111-1-1-12-2-22-1-1111-111-1-10000−i3i3i3−i3−i3i3i3−i300000000000000
χ382222-2-2-12-22-222-1-1-1-22-211-11111-1-1-12-2-22-1-1111-111-1-10000i3−i3−i3i3i3−i3−i3i300000000000000
χ392222-2-2-12-22-222-1-1-1-22-211-11111-1-1-1-222-211-1-11-1-1-1110000−i3i3i3−i3i3−i3−i3i300000000000000
χ402222-2-2-12-22-222-1-1-1-22-211-11111-1-1-1-222-211-1-11-1-1-1110000i3−i3−i3i3−i3i3i3−i300000000000000
χ412222-2-2-12-22-2-2-2-1-1-12-2211-111-1-111-12-22-2-1-111-11-1-1112-22-2-1-111-1-11100000000000000
χ422222-2-2-12-22-2-2-2-1-1-12-2211-111-1-111-12-22-2-1-111-11-1-111-22-2211-1-111-1-100000000000000
χ432222-2-2-12-22-2-2-2-1-1-12-2211-111-1-111-1-22-2211-1-1-1111-1-12-2-22-1-11111-1-100000000000000
χ442222-2-2-12-22-2-2-2-1-1-12-2211-111-1-111-1-22-2211-1-1-1111-1-1-222-211-1-1-1-11100000000000000
χ45444444-2-4-4-4-444-2-2-2-4-44-2-2222-2-2-2-220000000022000000000000000000000000000000
χ46444444-2-4-4-4-4-4-4-2-2-244-4-2-22222222200000000-2-2000000000000000000000000000000
χ474444-4-4-2-44-4444-2-2-24-4-4222-2-222-2-2200000000-22000000000000000000000000000000
χ484444-4-4-2-44-44-4-4-2-2-2-444222-2-2-2-2222000000002-2000000000000000000000000000000
χ4944-4-44-444-4-44004-4-40004-444-40000-40000000000000000000000000000000000000000
χ5044-4-44-44-444-4004-4-40004-4-4-44000040000000000000000000000000000000000000000
χ5144-4-44-4-24-4-4400-222000-22-2-22000020000−2i32i3−2i32i300000000000000000000000000000000
χ5244-4-44-4-24-4-4400-222000-22-2-220000200002i3−2i32i3−2i300000000000000000000000000000000
χ5344-4-44-4-2-444-400-222000-2222-20000-2000000000023−2323−2300000000000000000000000000
χ5444-4-44-4-2-444-400-222000-2222-20000-20000000000−2323−232300000000000000000000000000
χ5544-4-4-44444-4-4004-4-4000-444-440000-40000000000000000000000000000000000000000
χ5644-4-4-444-4-444004-4-4000-44-44-4000040000000000000000000000000000000000000000
χ5744-4-4-44-244-4-400-2220002-2-22-2000020000−2i32i32i3−2i300000000000000000000000000000000
χ5844-4-4-44-244-4-400-2220002-2-22-20000200002i3−2i3−2i32i300000000000000000000000000000000
χ5944-4-4-44-2-4-44400-2220002-22-220000-2000000000023−23−232300000000000000000000000000
χ6044-4-4-44-2-4-44400-2220002-22-220000-20000000000−232323−2300000000000000000000000000
χ614-44-400400004i−4i-44-400000000004i−4i000000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300
χ624-44-400400004i−4i-44-400000000004i−4i00000000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300
χ634-44-40040000−4i4i-44-40000000000−4i4i00000000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300
χ644-44-40040000−4i4i-44-40000000000−4i4i000000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300
χ658-88-800-400008i−8i4-440000000000−4i4i00000000000000000000000000000000000000000
χ668-88-800-40000−8i8i4-4400000000004i−4i00000000000000000000000000000000000000000
χ678-8-88008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-8-8800-400000044-400000000−4i34i30000000000000000000000000000000000000000000
χ698-8-8800-400000044-4000000004i3−4i30000000000000000000000000000000000000000000

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