Finite Group Databasebeta

← Group #10698932

Character table — Group #10698932

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order122222344444466644466121212121212121244441212121212121212121224668812122424242488888888888844
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
χ511111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-1
χ811111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ9222222222-2-2-2-22222-2-2222222-2-2-2-20000-2-20000000000000000000000002i2i−2i−2i000000
χ10222222222-2-2-2-22222-2-2222222-2-2-2-20000-2-2000000000000000000000000−2i−2i2i2i000000
χ112222222-2-22222222-2-2-222-2-2-2-2222222-2-2-2-22222-2-2-2-200000000000000000000000000
χ122222222-2-22222222-2-2-222-2-2-2-22222-2-222-2-2-2-2-2-2222200000000000000000000000000
χ132222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-2000022000000000000000000000000000022-2-200
χ142222222-2-2-2-2-2-2222-22222-2-2-2-2-2-2-2-20000220000000000000000000000000000-2-22200
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
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-11111111122-1-1-2-2-1-1111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-2-1-111111111-2-2112211-1-1-1-100000000000000
χ19222222-1-2-22222-1-1-1-2-2-2-1-11111-1-1-1-122-2-211-1-1-1-1111100−i3i300−i3i3−i3−i3i3i300000000000000
χ20222222-1-2-22222-1-1-1-2-2-2-1-11111-1-1-1-122-2-211-1-1-1-1111100i3−i300i3−i3i3i3−i3−i300000000000000
χ21222222-1-2-22222-1-1-1-2-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-100−i3i300−i3i3i3i3−i3−i300000000000000
χ22222222-1-2-22222-1-1-1-2-2-2-1-11111-1-1-1-1-2-222111111-1-1-1-100i3−i300i3−i3−i3−i3i3i300000000000000
χ232222-2-222222-2-2222-22-2-2-222-2-222-2-200002-2000000000000000000000000000000002i−2i
χ242222-2-222222-2-2222-22-2-2-222-2-222-2-200002-200000000000000000000000000000000−2i2i
χ252222-2-2222-2-222222-2-22-2-222-2-2-2-2220000-220000000000002-2002-22-200000000000000
χ262222-2-2222-2-222222-2-22-2-222-2-2-2-2220000-22000000000000-2200-22-2200000000000000
χ272222-2-22-2-222-2-22222-22-2-2-2-22222-2-20000-22000000000000000000002i2i−2i−2i0000000000
χ282222-2-22-2-222-2-22222-22-2-2-2-22222-2-20000-2200000000000000000000−2i−2i2i2i0000000000
χ292222-2-22-2-2-2-22222222-2-2-2-2-222-2-22200002-2000000002-22200-2-2000000000000000000
χ302222-2-22-2-2-2-22222222-2-2-2-2-222-2-22200002-200000000-22-2-20022000000000000000000
χ312222-2-2-122-2-222-1-1-1-2-2211-1-11111-1-100001-1−i3−i3i3i3−i3−i3i3i300−i3i32-2i3−i3-11-1100000000000000
χ322222-2-2-122-2-222-1-1-1-2-2211-1-11111-1-100001-1−i3−i3i3i3−i3−i3i3i300i3−i3-22−i3i31-11-100000000000000
χ332222-2-2-122-2-222-1-1-1-2-2211-1-11111-1-100001-1i3i3−i3−i3i3i3−i3−i300−i3i3-22i3−i31-11-100000000000000
χ342222-2-2-122-2-222-1-1-1-2-2211-1-11111-1-100001-1i3i3−i3−i3i3i3−i3−i300i3−i32-2−i3i3-11-1100000000000000
χ352222-2-2-1-2-2-2-222-1-1-122-21111-1-111-1-10000-11−i3−i3i3i3i3i3−i3−i32-2-1-10011−i3i3i3−i300000000000000
χ362222-2-2-1-2-2-2-222-1-1-122-21111-1-111-1-10000-11−i3−i3i3i3i3i3−i3−i3-221100-1-1i3−i3−i3i300000000000000
χ372222-2-2-1-2-2-2-222-1-1-122-21111-1-111-1-10000-11i3i3−i3−i3−i3−i3i3i32-2-1-10011i3−i3−i3i300000000000000
χ382222-2-2-1-2-2-2-222-1-1-122-21111-1-111-1-10000-11i3i3−i3−i3−i3−i3i3i3-221100-1-1−i3i3i3−i300000000000000
χ392-2-22-222002-22-2-2-220002-200002-22-22i−2i00002i−2i2i−2i00000000000000000000−i2i2−i2i22−22−200
χ402-2-22-222002-22-2-2-220002-200002-22-22i−2i00002i−2i2i−2i00000000000000000000i2−i2i2−i2−22−2200
χ412-2-22-222002-22-2-2-220002-200002-22-2−2i2i0000−2i2i−2i2i00000000000000000000−i2i2−i2i2−22−2200
χ422-2-22-222002-22-2-2-220002-200002-22-2−2i2i0000−2i2i−2i2i00000000000000000000i2−i2i2−i22−22−200
χ432-2-22-22200-22-22-2-220002-20000-22-22002-20000002-22-200000000000000002−2−222−2−2200
χ442-2-22-22200-22-22-2-220002-20000-22-22002-20000002-22-20000000000000000−222−2−222−200
χ452-2-22-22200-22-22-2-220002-20000-22-2200-22000000-22-2200000000000000002−2−22−222−200
χ462-2-22-22200-22-22-2-220002-20000-22-2200-22000000-22-220000000000000000−222−22−2−2200
χ47444444-244-4-4-4-4-2-2-24-4-4-2-2-2-2-2-222220000220000000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-2-444-2-2222222220000-2-20000000000000000000000000000000000
χ494444-4-4-24444-4-4-2-2-2-44-422-2-222-2-2220000-220000000000000000000000000000000000
χ504444-4-4-2-4-444-4-4-2-2-24-442222-2-2-2-22200002-20000000000000000000000000000000000
χ514-44-40044i−4i0000-44-4000004i−4i000000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000
χ524-44-40044i−4i0000-44-4000004i−4i00000000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000
χ534-44-4004−4i4i0000-44-400000−4i4i00000000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000
χ544-44-4004−4i4i0000-44-400000−4i4i000000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000
χ554-4-444-44004-4-44-4-44000-4400004-4-440000000000000000000000000000000000000000
χ564-4-444-4400-444-4-4-44000-440000-444-40000000000000000000000000000000000000000
χ574-4-444-4-2004-4-4422-20002-20000-222-20000000000−2i32i32i3−2i300000000000000000000000000
χ584-4-444-4-2004-4-4422-20002-20000-222-200000000002i3−2i3−2i32i300000000000000000000000000
χ594-4-444-4-200-444-422-20002-200002-2-2200000023−23−2323000000000000000000000000000000
χ604-4-444-4-200-444-422-20002-200002-2-22000000−232323−23000000000000000000000000000000
χ614-4-44-44-2004-44-422-2000-220000-22-224i−4i0000−2i2i−2i2i000000000000000000000000000000
χ624-4-44-44-2004-44-422-2000-220000-22-22−4i4i00002i−2i2i−2i000000000000000000000000000000
χ634-4-44-44-200-44-4422-2000-2200002-22-2004-4000000-22-2200000000000000000000000000
χ644-4-44-44-200-44-4422-2000-2200002-22-200-440000002-22-200000000000000000000000000
χ6588-8-80080000008-8-800000000000000000000000000000000000000000000000000000
χ6688-8-800-4000000-4440000000−4i34i300000000000000000000000000000000000000000000
χ6788-8-800-4000000-44400000004i3−4i300000000000000000000000000000000000000000000
χ688-88-800-48i−8i00004-4400000−4i4i0000000000000000000000000000000000000000000000
χ698-88-800-4−8i8i00004-44000004i−4i0000000000000000000000000000000000000000000000

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