Finite Group Databasebeta

← Group #10897657

Character table — Group #10897657

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444466668888888888881212121212121212121216161616161616161616161616162424242424244848
order124422234446121266688881212124444222444882424242444888888886668812121224242424242444888844
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-11-1-111111111111111111-1-1-1-11-1-111-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111111-11-1-11-1-1-1111111-1-1-1-11111-11-11-1-11-1-1-111-1-1-1-111-1-11-1
χ41111111111111111111111111111-1-11-1-11-1-1111111-1-1-1-11111-1-11-11-1-11-1-1-1-111-1-1-1-111-11
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11-1-11-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-111-1-1-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-11-1-11-1-1-11111-1-11111-1-1-1-1-11-11-1-11-1-1-111-1-111-1-111-11
χ8111111111111111111111111-1-1-1-1-1-11-1-11-1-11111-1-11111-1-1-1-1-1-11-11-1-11-1-1-1-1111111-1-11-1
χ911111111111111111-1-1-1-1111111111-111-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1111-1-1-1-1-1111111-1-1-11
χ1011111111111111111-1-1-1-111111111-111-11-1-1-1-1-1-111-1-1-1-1-1-1-1-11-111-11-11-1-111-1-111-1-1111-1
χ1111111111111111111-1-1-1-11111111-111-11111-1-1-1-1111111-1-1-1-1-111-1-1-11111-1-1-1-1-1-11111-1-1
χ1211111111111111111-1-1-1-11111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1111111-1-1-1-1-1-111
χ1311111111111111111-1-1-1-1111-1-1-1-111-111-1-1-1-1-1-1-1-1-11111111111-1-1111-1-1-1-1-111-1-1-1-1111-1
χ1411111111111111111-1-1-1-1111-1-1-1-11-111-11-1-1-1-1-1-1-1-1111111111-111-11-11-1-111-1-1-1-111-1-1-11
χ1511111111111111111-1-1-1-1111-1-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1-1-111-1-1-1-111
χ1611111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1111111111111-1-1
χ172222222-1222-1-1-1-1-1-12222-1-1-1000022222222-1-1-1-10000000000-1-1-122-1-1-1-1-1-1-1-1-100000000
χ182222222-1222-1-1-1-1-1-12222-1-1-100002-2-22-2-222-1-1-1-10000000000-111-2-2-111-1-1111100000000
χ192222222-1222-1-1-1-1-1-12222-1-1-10000-22-2-22-2-2-2-1-1-1-100000000001-112-21-1111-1-11100000000
χ202222222-1222-1-1-1-1-1-12222-1-1-10000-2-22-2-22-2-2-1-1-1-1000000000011-1-2211-11111-1-100000000
χ212222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-1000022-222-2-2-211110000000000-1-11-22-1-111111-1-100000000
χ222222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-100002-222-22-2-211110000000000-11-12-2-11-111-1-11100000000
χ232222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-10000-222-22222111100000000001-1-1-2-21-1-1-1-1111100000000
χ242222222-1222-1-1-1-1-1-1-2-2-2-2-1-1-10000-2-2-2-2-2-2221111000000000011122111-1-1-1-1-1-100000000
χ252222-2-222-2-222222-2-200002-2-222220000002-20000-2-222-2-20000000000002-2000000000000
χ262222-2-222-2-222222-2-200002-2-22222000000-220000-2-2-2-222000000000000-22000000000000
χ272222-2-222-2-222222-2-200002-2-2-2-2-2-20000002-2000022-2-2220000000000002-2000000000000
χ282222-2-222-2-222222-2-200002-2-2-2-2-2-2000000-2200002222-2-2000000000000-22000000000000
χ2922-2-22222-2-2-22-2-22222i2i−2i−2i-2-2-20000000000002i2i−2i−2i002i−2i2i−2i0000000000000000002-2000000
χ3022-2-22222-2-2-22-2-22222i2i−2i−2i-2-2-20000000000002i2i−2i−2i00−2i2i−2i2i000000000000000000-22000000
χ3122-2-22222-2-2-22-2-2222−2i−2i2i2i-2-2-2000000000000−2i−2i2i2i002i−2i2i−2i000000000000000000-22000000
χ3222-2-22222-2-2-22-2-2222−2i−2i2i2i-2-2-2000000000000−2i−2i2i2i00−2i2i−2i2i0000000000000000002-2000000
χ3322-2-22-2-222-222-2-2-22-2000022-22i2i−2i−2i00200-20000002i−2i000000000020000-200000000002i−2i00
χ3422-2-22-2-222-222-2-2-22-2000022-22i2i−2i−2i00-20020000002i−2i0000000000-2000020000000000−2i2i00
χ3522-2-22-2-222-222-2-2-22-2000022-2−2i−2i2i2i00200-2000000−2i2i000000000020000-20000000000−2i2i00
χ3622-2-22-2-222-222-2-2-22-2000022-2−2i−2i2i2i00-2002000000−2i2i0000000000-20000200000000002i−2i00
χ3722-2-2-22-22-2222-2-2-2-2200002-222i2i−2i−2i0200-20000000−2i2i00000000020000-20000000002i−2i0000
χ3822-2-2-22-22-2222-2-2-2-2200002-222i2i−2i−2i0-20020000000−2i2i000000000-200002000000000−2i2i0000
χ3922-2-2-22-22-2222-2-2-2-2200002-22−2i−2i2i2i0200-200000002i−2i00000000020000-2000000000−2i2i0000
χ4022-2-2-22-22-2222-2-2-2-2200002-22−2i−2i2i2i0-200200000002i−2i000000000-2000020000000002i−2i0000
χ4122-2-2-2-22222-22-2-22-2-20000-2220000200-200000000002i−2i−2i2i2i2i−2i−2i20000-20000000000000000
χ4222-2-2-2-22222-22-2-22-2-20000-2220000200-20000000000−2i2i2i−2i−2i−2i2i2i20000-20000000000000000
χ4322-2-2-2-22222-22-2-22-2-20000-2220000-200200000000002i−2i−2i2i−2i−2i2i2i-2000020000000000000000
χ4422-2-2-2-22222-22-2-22-2-20000-2220000-20020000000000−2i2i2i−2i2i2i−2i−2i-2000020000000000000000
χ4544444-4-44-44-4444-44-40000-4-44000000000000000000000000000000000000000000000000
χ4644444-4-4-2-44-4-2-2-22-22000022-200000000000000000000000000000000000000−2i32i300000000
χ4744444-4-4-2-44-4-2-2-22-22000022-2000000000000000000000000000000000000002i3−2i300000000
χ484444-44-444-4-4444-4-440000-44-4000000000000000000000000000000000000000000000000
χ494444-44-4-24-4-4-2-2-222-200002-22000000000000000000000000000000000000−2i32i30000000000
χ504444-44-4-24-4-4-2-2-222-200002-220000000000000000000000000000000000002i3−2i30000000000
χ514444-4-44-2-4-44-2-2-2-2220000-22200000000004-40000000000000000000000-22000000000000
χ524444-4-44-2-4-44-2-2-2-2220000-2220000000000-4400000000000000000000002-2000000000000
χ5344-4-4444-2-4-4-4-222-2-2-24i4i−4i−4i222000000000000−2i−2i2i2i00000000000000000000000000000000
χ5444-4-4444-2-4-4-4-222-2-2-2−4i−4i4i4i2220000000000002i2i−2i−2i00000000000000000000000000000000
χ5544-4-44-4-4-24-44-2222-220000-2-22000000400-4000000000000000000-20000200000000000000
χ5644-4-44-4-4-24-44-2222-220000-2-22000000-400400000000000000000020000-200000000000000
χ5744-4-4-44-4-2-444-22222-20000-22-200000400-4000000000000000000-200002000000000000000
χ5844-4-4-44-4-2-444-22222-20000-22-200000-400400000000000000000020000-2000000000000000
χ5944-4-4-4-44-244-4-222-22200002-2-20000400-4000000000000000000-2000020000000000000000
χ6044-4-4-4-44-244-4-222-22200002-2-20000-400400000000000000000020000-20000000000000000
χ614-44i−4i0004000-44i−4i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130002+2i−2−2i2−2i−2+2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ624-44i−4i0004000-44i−4i0002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000−2−2i2+2i−2+2i2−2i000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ13000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ634-44i−4i0004000-44i−4i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130002+2i−2−2i2−2i−2+2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000
χ644-44i−4i0004000-44i−4i000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ13000−2−2i2+2i−2+2i2−2i00000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000
χ654-4−4i4i0004000-4−4i4i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230002−2i−2+2i2+2i−2−2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ664-4−4i4i0004000-4−4i4i000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ23000−2+2i2−2i−2−2i2+2i00000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ674-4−4i4i0004000-4−4i4i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230002−2i−2+2i2+2i−2−2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000
χ684-4−4i4i0004000-4−4i4i0002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000−2+2i2−2i−2−2i2+2i000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ23000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000
χ698-88i−8i000-40004−4i4i0004ζ7+4ζ23−4ζ7−4ζ23−4ζ5−4ζ134ζ5+4ζ13000000000000000−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ1300000000000000000000000000000000
χ708-88i−8i000-40004−4i4i000−4ζ7−4ζ234ζ7+4ζ234ζ5+4ζ13−4ζ5−4ζ130000000000000002ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ1300000000000000000000000000000000
χ718-8−8i8i000-400044i−4i000−4ζ5−4ζ134ζ5+4ζ134ζ7+4ζ23−4ζ7−4ζ230000000000000002ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000
χ728-8−8i8i000-400044i−4i0004ζ5+4ζ13−4ζ5−4ζ13−4ζ7−4ζ234ζ7+4ζ23000000000000000−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000

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