Finite Group Databasebeta

← Group #10697656

Character table — Group #10697656

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1111222222222222224444444444448888888888888812121212121212121616161616161616161616162424242448484848
order12222234444444466644661212121212121212224466661212121212128888888824668812122424242488882488
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-111
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-111-1-1
χ7111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111
χ922222222-2-2-2222-2222-2-2222222-2-2-2-200000000-2-200000000000000000000000022-2-20000
χ1022222222-2-2-2222-2222-2-2222222-2-2-2-200000000-2-2000000000000000000000000-2-2220000
χ112222222-2222-2-2-22222-2-222-2-2-2-2222222-2-22222-2-2-2-2-2-20000000000000000000000000000
χ122222222-2222-2-2-22222-2-222-2-2-2-22222-2-222-2-2-2-2-2-222220000000000000000000000000000
χ132222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002200002i2i2i2i−2i−2i−2i−2i00000000000000000000
χ142222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-200000000220000−2i−2i−2i−2i2i2i2i2i00000000000000000000
χ15222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000000022-1-122-1-1-1-1-1-100000000
χ16222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-100000000-2-211-2-211111100000000
χ17222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-111110000000022-1-1-2-2-1-1111100000000
χ18222222-122222222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111100000000-2-2112211-1-1-1-100000000
χ19222222-1-2222-2-2-22-1-1-1-2-2-1-11111-1-1-1-122-2-2-1-1-1-11111110000000000−i3i300−i3i3−i3−i3i3i300000000
χ20222222-1-2222-2-2-22-1-1-1-2-2-1-11111-1-1-1-122-2-2-1-1-1-11111110000000000i3−i300i3−i3i3i3−i3−i300000000
χ21222222-1-2222-2-2-22-1-1-1-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-10000000000−i3i300−i3i3i3i3−i3−i300000000
χ22222222-1-2222-2-2-22-1-1-1-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-10000000000i3−i300i3−i3−i3−i3i3i300000000
χ232222-2-2222-22-2-22-22222-2-2-222-2-22-2-22000000002-20000000000002-22200-2-2000000000000
χ242222-2-2222-22-2-22-22222-2-2-222-2-22-2-22000000002-2000000000000-22-2-20022000000000000
χ252222-2-222-22-2-2-222222-22-2-222-2-2-222-200000000-2200000000000000000000000000002-200
χ262222-2-222-22-2-2-222222-22-2-222-2-2-222-200000000-220000000000000000000000000000-2200
χ272222-2-22-22-2222-2-2222-22-2-2-2-2222-2-2200000000-2200000000000000002-2002-22-200000000
χ282222-2-22-22-2222-2-2222-22-2-2-2-2222-2-2200000000-220000000000000000-2200-22-2200000000
χ292222-2-22-2-22-222-222222-2-2-2-2-222-222-2000000002-20000000000000000000000000000002-2
χ302222-2-22-2-22-222-222222-2-2-2-2-222-222-2000000002-2000000000000000000000000000000-22
χ312222-2-2-122-22-2-22-2-1-1-12-211-1-111-111-10000−i3−i3i3i3-11−i3−i3i3i3000000002-2-1-10011−i3i3i3−i300000000
χ322222-2-2-122-22-2-22-2-1-1-12-211-1-111-111-10000−i3−i3i3i3-11−i3−i3i3i300000000-221100-1-1i3−i3−i3i300000000
χ332222-2-2-122-22-2-22-2-1-1-12-211-1-111-111-10000i3i3−i3−i3-11i3i3−i3−i3000000002-2-1-10011i3−i3−i3i300000000
χ342222-2-2-122-22-2-22-2-1-1-12-211-1-111-111-10000i3i3−i3−i3-11i3i3−i3−i300000000-221100-1-1−i3i3i3−i300000000
χ352222-2-2-1-22-2222-2-2-1-1-1-221111-1-1-111-10000−i3−i3i3i31-1i3i3−i3−i30000000000−i3i32-2i3−i3-11-1100000000
χ362222-2-2-1-22-2222-2-2-1-1-1-221111-1-1-111-10000−i3−i3i3i31-1i3i3−i3−i30000000000i3−i3-22−i3i31-11-100000000
χ372222-2-2-1-22-2222-2-2-1-1-1-221111-1-1-111-10000i3i3−i3−i31-1−i3−i3i3i30000000000−i3i3-22i3−i31-11-100000000
χ382222-2-2-1-22-2222-2-2-1-1-1-221111-1-1-111-10000i3i3−i3−i31-1−i3−i3i3i30000000000i3−i32-2−i3i3-11-1100000000
χ392-2-222-22022-2000-2-22-2002-2000022-2-2002i−2i0000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i20000000000002−22−20000
χ402-2-222-22022-2000-2-22-2002-2000022-2-2002i−2i0000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i2000000000000−22−220000
χ412-2-222-22022-2000-2-22-2002-2000022-2-200−2i2i000000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i2000000000000−22−220000
χ422-2-222-22022-2000-2-22-2002-2000022-2-200−2i2i000000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i20000000000002−22−20000
χ432-2-222-220-2-220002-22-2002-20000-2-2222-2002-22-200000022−2−2−2−2220000000000002−2−220000
χ442-2-222-220-2-220002-22-2002-20000-2-2222-2002-22-2000000−2−22222−2−2000000000000−222−20000
χ452-2-222-220-2-220002-22-2002-20000-2-222-2200-22-2200000022−2−2−2−222000000000000−222−20000
χ462-2-222-220-2-220002-22-2002-20000-2-222-2200-22-22000000−2−22222−2−20000000000002−2−220000
χ47444444-24-4-4-4444-4-2-2-2-4-4-2-2-2-2-2-22222000000002200000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-4-4-2-2-244-2-22222222200000000-2-200000000000000000000000000000000
χ494444-4-4-24-44-4-4-444-2-2-2-4422-2-2222-2-22000000002-200000000000000000000000000000000
χ504444-4-4-2-4-44-444-44-2-2-24-42222-2-22-2-2200000000-2200000000000000000000000000000000
χ5144-4-400400004i−4i004-4-40000004i−4i0000000000000000002ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ1300000000000000000000
χ5244-4-400400004i−4i004-4-40000004i−4i000000000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ1300000000000000000000
χ5344-4-40040000−4i4i004-4-4000000−4i4i000000000000000000−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ2300000000000000000000
χ5444-4-40040000−4i4i004-4-4000000−4i4i0000000000000000002ζ5+2ζ13−2ζ5−2ζ132ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23−2ζ7−2ζ232ζ7+2ζ2300000000000000000000
χ554-44-4004400000-40-4-4400004-4000000000000000000002i−2i−2i2i2i−2i−2i2i00000000000000000000
χ564-44-4004400000-40-4-4400004-400000000000000000000−2i2i2i−2i−2i2i2i−2i00000000000000000000
χ574-44-4004-40000040-4-440000-44000000000000000000002-2-22-222-200000000000000000000
χ584-44-4004-40000040-4-440000-4400000000000000000000-222-22-2-2200000000000000000000
χ594-4-444-4-2044-4000-42-2200-220000-2-222004i−4i000000−2i2i−2i2i0000000000000000000000000000
χ604-4-444-4-2044-4000-42-2200-220000-2-22200−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ614-4-444-4-20-4-4400042-2200-22000022-2-24-400-22-220000000000000000000000000000000000
χ624-4-444-4-20-4-4400042-2200-22000022-2-2-44002-22-20000000000000000000000000000000000
χ634-4-44-44404-4-40004-44-400-4400004-44-4000000000000000000000000000000000000000000
χ644-4-44-4440-444000-4-44-400-440000-44-44000000000000000000000000000000000000000000
χ654-4-44-44-204-4-400042-22002-20000-22-22000000000023−23−23230000000000000000000000000000
χ664-4-44-44-204-4-400042-22002-20000-22-220000000000−232323−230000000000000000000000000000
χ674-4-44-44-20-444000-42-22002-200002-22-20000−2i32i32i3−2i30000000000000000000000000000000000
χ684-4-44-44-20-444000-42-22002-200002-22-200002i3−2i3−2i32i30000000000000000000000000000000000
χ6988-8-800-400008i−8i00-444000000−4i4i0000000000000000000000000000000000000000000000
χ7088-8-800-40000−8i8i00-4440000004i−4i0000000000000000000000000000000000000000000000
χ718-88-800-4800000-8044-40000-44000000000000000000000000000000000000000000000000
χ728-88-800-4-8000008044-400004-4000000000000000000000000000000000000000000000000

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