Finite Group Databasebeta

← Group #10698946

Character table — Group #10698946

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69
size11112222222222224444444444444888888888888881616161616161616161616162424242424242424242424244848
order1222223444444666444661212121212121212224466661212121212124488121212122424242488888888888844
χ1111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ41111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ611111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111
χ711111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11111-1-1
χ811111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111
χ9222222222-2-222222-2-2-222222-2-2-2-2222-2-22222-2-2-2-2-2-200000000000000000000000000
χ10222222222-2-222222-2-2-222222-2-2-2-22-2-222-2-2-2-2-2-2222200000000000000000000000000
χ112222222-2-222-2-22222-2-222-2-2-22222-200000000-2-2000000000000000000002i2i−2i−2i000000
χ122222222-2-222-2-22222-2-222-2-2-22222-200000000-2-200000000000000000000−2i−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
χ15222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000000000
χ16222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111100000000000000
χ17222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-1111122-2-2-1-1-1-1111100000000000000
χ18222222-1222222-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-2-2-21111-1-11111-2-2221111-1-1-1-100000000000000
χ19222222-122-2-222-1-1-1-2-2-2-1-1-1-1-11111-122-2-2-1-1-1-11111110000−i3i3−i3i3−i3−i3i3i300000000000000
χ20222222-122-2-222-1-1-1-2-2-2-1-1-1-1-11111-122-2-2-1-1-1-11111110000i3−i3i3−i3i3i3−i3−i300000000000000
χ21222222-122-2-222-1-1-1-2-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-10000−i3i3−i3i3i3i3−i3−i300000000000000
χ22222222-122-2-222-1-1-1-2-2-2-1-1-1-1-11111-1-2-222111111-1-1-1-10000i3−i3i3−i3−i3−i3i3i300000000000000
χ232222-2-222222-2-2222-22-2-2-222-222-2-2-2000000002-200000000000000000000000000002i−2i
χ242222-2-222222-2-2222-22-2-2-222-222-2-2-2000000002-20000000000000000000000000000−2i2i
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
χ272222-2-22-2-22222222-2-22-2-2-2-2222-2-2200000000-220000002-200002-22-200000000000000
χ282222-2-22-2-22222222-2-22-2-2-2-2222-2-2200000000-22000000-220000-22-2200000000000000
χ292222-2-22-2-2-2-22222222-2-2-2-2-22-2-2222000000002-200002-20022-2-2000000000000000000
χ302222-2-22-2-2-2-22222222-2-2-2-2-22-2-2222000000002-20000-2200-2-222000000000000000000
χ312222-2-2-1-2-22222-1-1-1-2-221111-1-1-111-10000−i3−i3i3i31-1−i3−i3i3i3002-2−i3i3i3−i3-11-1100000000000000
χ322222-2-2-1-2-22222-1-1-1-2-221111-1-1-111-10000−i3−i3i3i31-1−i3−i3i3i300-22i3−i3−i3i31-11-100000000000000
χ332222-2-2-1-2-22222-1-1-1-2-221111-1-1-111-10000i3i3−i3−i31-1i3i3−i3−i3002-2i3−i3−i3i3-11-1100000000000000
χ342222-2-2-1-2-22222-1-1-1-2-221111-1-1-111-10000i3i3−i3−i31-1i3i3−i3−i300-22−i3i3i3−i31-11-100000000000000
χ352222-2-2-1-2-2-2-222-1-1-122-21111-111-1-1-10000−i3−i3i3i3-11i3i3−i3−i32-200-1-111−i3i3i3−i300000000000000
χ362222-2-2-1-2-2-2-222-1-1-122-21111-111-1-1-10000−i3−i3i3i3-11i3i3−i3−i3-220011-1-1i3−i3−i3i300000000000000
χ372222-2-2-1-2-2-2-222-1-1-122-21111-111-1-1-10000i3i3−i3−i3-11−i3−i3i3i32-200-1-111i3−i3−i3i300000000000000
χ382222-2-2-1-2-2-2-222-1-1-122-21111-111-1-1-10000i3i3−i3−i3-11−i3−i3i3i3-220011-1-1−i3i3i3−i300000000000000
χ3922-2-2-2222-2002-22-2-20002-22-2-200002002i−2i0000002i−2i2i−2i00000000000000002−22−2−i2i2−i2i200
χ4022-2-2-2222-2002-22-2-20002-22-2-200002002i−2i0000002i−2i2i−2i0000000000000000−22−22i2−i2i2−i200
χ4122-2-2-2222-2002-22-2-20002-22-2-20000200−2i2i000000−2i2i−2i2i00000000000000002−22−2i2−i2i2−i200
χ4222-2-2-2222-2002-22-2-20002-22-2-20000200−2i2i000000−2i2i−2i2i0000000000000000−22−22−i2i2−i2i200
χ4322-2-2-222-2200-222-2-20002-2-2220000-22-2002-22-20000000000000000000000−i2i2i2−i2−i2i2i2−i200
χ4422-2-2-222-2200-222-2-20002-2-2220000-22-2002-22-20000000000000000000000i2−i2−i2i2i2−i2−i2i200
χ4522-2-2-222-2200-222-2-20002-2-2220000-2-2200-22-220000000000000000000000−i2i2i2−i2i2−i2−i2i200
χ4622-2-2-222-2200-222-2-20002-2-2220000-2-2200-22-220000000000000000000000i2−i2−i2i2−i2i2i2−i200
χ47444444-2-4-444-4-4-2-2-24-4-4-2-2222-2-2-2-220000000022000000000000000000000000000000
χ48444444-2-4-4-4-4-4-4-2-2-2-444-2-22222222200000000-2-2000000000000000000000000000000
χ494444-4-4-24444-4-4-2-2-2-44-422-2-22-2-222200000000-22000000000000000000000000000000
χ504444-4-4-244-4-4-4-4-2-2-24-4422-2-2222-2-22000000002-2000000000000000000000000000000
χ5144-4-44-444-400-444-4-4000-444-440000-40000000000000000000000000000000000000000
χ5244-4-44-44-44004-44-4-4000-44-44-4000040000000000000000000000000000000000000000
χ5344-4-44-4-24-400-44-2220002-2-22-2000020000−2i32i32i3−2i300000000000000000000000000000000
χ5444-4-44-4-24-400-44-2220002-2-22-20000200002i3−2i3−2i32i300000000000000000000000000000000
χ5544-4-44-4-2-44004-4-2220002-22-220000-2000000000023−23−232300000000000000000000000000
χ5644-4-44-4-2-44004-4-2220002-22-220000-20000000000−232323−2300000000000000000000000000
χ5744-4-4-44-24-4004-4-222000-22-2220000-2004i−4i000000−2i2i−2i2i00000000000000000000000000
χ5844-4-4-44-24-4004-4-222000-22-2220000-200−4i4i0000002i−2i2i−2i00000000000000000000000000
χ5944-4-4-44-2-4400-44-222000-222-2-2000024-400-22-2200000000000000000000000000000000
χ6044-4-4-44-2-4400-44-222000-222-2-200002-44002-22-200000000000000000000000000000000
χ614-44-4004004i−4i00-44-4000000004i−4i000000000000000000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000
χ624-44-4004004i−4i00-44-4000000004i−4i00000000000000000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000
χ634-44-400400−4i4i00-44-400000000−4i4i00000000000000000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000
χ644-44-400400−4i4i00-44-400000000−4i4i000000000000000000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000
χ658-88-800-4008i−8i004-4400000000−4i4i0000000000000000000000000000000000000000000
χ668-88-800-400−8i8i004-44000000004i−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.