Finite Group Databasebeta

← Group #10698918

Character table — Group #10698918

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order12222234444446664446612121212121212122244666612121212121224668812122424242488888888888844
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
χ511111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ92222222222-2-22222-2-2-222222-2-2-2-2222-2-22222-2-2-2-2-2-200000000000000000000000000
χ102222222222-2-22222-2-2-222222-2-2-2-22-2-222-2-2-2-2-2-2222200000000000000000000000000
χ112222222-2-2-222-22222-2-222-2-2-22222-200000000-2-2000000000000000000002i2i−2i−2i000000
χ122222222-2-2-222-22222-2-222-2-2-22222-200000000-2-200000000000000000000−2i−2i2i2i000000
χ132222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-2000000002200000000000000000000000022-2-200
χ142222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-20000000022000000000000000000000000-2-22200
χ15222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-122-1-122-1-1-1-1-1-100000000000000
χ16222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-211-2-211111100000000000000
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111122-1-1-2-2-1-1111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-11111-2-2112211-1-1-1-100000000000000
χ19222222-1222-2-22-1-1-1-2-2-2-1-1-1-1-11111-122-2-2-1-1-1-111111100−i3i300−i3i3−i3−i3i3i300000000000000
χ20222222-1222-2-22-1-1-1-2-2-2-1-1-1-1-11111-122-2-2-1-1-1-111111100i3−i300i3−i3i3i3−i3−i300000000000000
χ21222222-1222-2-22-1-1-1-2-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-100−i3i300−i3i3i3i3−i3−i300000000000000
χ22222222-1222-2-22-1-1-1-2-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-100i3−i300i3−i3−i3−i3i3i300000000000000
χ232222-2-2222-222-2222-22-2-2-222-222-2-2-2000000002-200000000000000000000000000002i−2i
χ242222-2-2222-222-2222-22-2-2-222-222-2-2-2000000002-20000000000000000000000000000−2i2i
χ252222-2-2222-2-2-2-22222-22-2-222-2-2-222-200000000-2200000000000000002i2i−2i−2i0000000000
χ262222-2-2222-2-2-2-22222-22-2-222-2-2-222-200000000-220000000000000000−2i−2i2i2i0000000000
χ272222-2-22-2-22222222-2-22-2-2-2-2222-2-2200000000-22000000002-2002-22-200000000000000
χ282222-2-22-2-22222222-2-22-2-2-2-2222-2-2200000000-2200000000-2200-22-2200000000000000
χ292222-2-22-2-22-2-2222222-2-2-2-2-22-2-2222000000002-200002-22200-2-2000000000000000000
χ302222-2-22-2-22-2-2222222-2-2-2-2-22-2-2222000000002-20000-22-2-20022000000000000000000
χ312222-2-2-1-2-22222-1-1-1-2-221111-1-1-111-10000−i3−i3i3i31-1−i3−i3i3i300−i3i32-2i3−i3-11-1100000000000000
χ322222-2-2-1-2-22222-1-1-1-2-221111-1-1-111-10000−i3−i3i3i31-1−i3−i3i3i300i3−i3-22−i3i31-11-100000000000000
χ332222-2-2-1-2-22222-1-1-1-2-221111-1-1-111-10000i3i3−i3−i31-1i3i3−i3−i300−i3i3-22i3−i31-11-100000000000000
χ342222-2-2-1-2-22222-1-1-1-2-221111-1-1-111-10000i3i3−i3−i31-1i3i3−i3−i300i3−i32-2−i3i3-11-1100000000000000
χ352222-2-2-1-2-22-2-22-1-1-122-21111-111-1-1-10000−i3−i3i3i3-11i3i3−i3−i32-2-1-10011−i3i3i3−i300000000000000
χ362222-2-2-1-2-22-2-22-1-1-122-21111-111-1-1-10000−i3−i3i3i3-11i3i3−i3−i3-221100-1-1i3−i3−i3i300000000000000
χ372222-2-2-1-2-22-2-22-1-1-122-21111-111-1-1-10000i3i3−i3−i3-11−i3−i3i3i32-2-1-10011i3−i3−i3i300000000000000
χ382222-2-2-1-2-22-2-22-1-1-122-21111-111-1-1-10000i3i3−i3−i3-11−i3−i3i3i3-221100-1-1−i3i3i3−i300000000000000
χ392-22-2-2222-2200-2-22-20002-22-220000-2002i−2i0000002i−2i2i−2i0000000000000000−i2i2−i2i22−22−200
χ402-22-2-2222-2200-2-22-20002-22-220000-2002i−2i0000002i−2i2i−2i0000000000000000i2−i2i2−i2−22−2200
χ412-22-2-2222-2200-2-22-20002-22-220000-200−2i2i000000−2i2i−2i2i0000000000000000−i2i2−i2i2−22−2200
χ422-22-2-2222-2200-2-22-20002-22-220000-200−2i2i000000−2i2i−2i2i0000000000000000i2−i2i2−i22−22−200
χ432-22-2-222-22-2002-22-20002-2-22-2000022-2002-22-200000000000000000000002−2−222−2−2200
χ442-22-2-222-22-2002-22-20002-2-22-2000022-2002-22-20000000000000000000000−222−2−222−200
χ452-22-2-222-22-2002-22-20002-2-22-200002-2200-22-2200000000000000000000002−2−22−222−200
χ462-22-2-222-22-2002-22-20002-2-22-200002-2200-22-220000000000000000000000−222−22−2−2200
χ47444444-2-4-4-444-4-2-2-24-4-4-2-2222-2-2-2-220000000022000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-2-444-2-22222222200000000-2-2000000000000000000000000000000
χ494444-4-4-244-444-4-2-2-2-44-422-2-22-2-222200000000-22000000000000000000000000000000
χ504444-4-4-244-4-4-4-4-2-2-24-4422-2-2222-2-22000000002-2000000000000000000000000000000
χ5144-4-40040004i−4i04-4-4000000004i−4i000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000
χ5244-4-40040004i−4i04-4-4000000004i−4i00000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000
χ5344-4-4004000−4i4i04-4-400000000−4i4i00000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000
χ5444-4-4004000−4i4i04-4-400000000−4i4i000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000
χ554-44-44-444-4-4004-44-4000-444-4-4000040000000000000000000000000000000000000000
χ564-44-44-44-44400-4-44-4000-44-4440000-40000000000000000000000000000000000000000
χ574-44-44-4-24-4-40042-220002-2-2220000-20000−2i32i32i3−2i300000000000000000000000000000000
χ584-44-44-4-24-4-40042-220002-2-2220000-200002i3−2i3−2i32i300000000000000000000000000000000
χ594-44-44-4-2-44400-42-220002-22-2-200002000000000023−23−232300000000000000000000000000
χ604-44-44-4-2-44400-42-220002-22-2-2000020000000000−232323−2300000000000000000000000000
χ614-44-4-44-24-4400-42-22000-22-22-200002004i−4i000000−2i2i−2i2i00000000000000000000000000
χ624-44-4-44-24-4400-42-22000-22-22-20000200−4i4i0000002i−2i2i−2i00000000000000000000000000
χ634-44-4-44-2-44-40042-22000-222-220000-24-400-22-2200000000000000000000000000000000
χ644-44-4-44-2-44-40042-22000-222-220000-2-44002-22-200000000000000000000000000000000
χ6588-8-800-40008i−8i0-44400000000−4i4i0000000000000000000000000000000000000000000
χ6688-8-800-4000−8i8i0-444000000004i−4i0000000000000000000000000000000000000000000
χ678-8-88008000000-8-8800000000000000000000000000000000000000000000000000000
χ688-8-8800-400000044-40000000000−4i34i300000000000000000000000000000000000000000
χ698-8-8800-400000044-400000000004i3−4i300000000000000000000000000000000000000000

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