Finite Group Databasebeta

← Group #10896439

Character table — Group #10896439

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size11112222222222444444444466668888888888881212121212121212121216161616161616161616161616162424242424244848
order12442223444612124444666121212888824444488121212128888888888468121212121212122424242424888848
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-111-1111-1-1-1-1-1-1-1-11111-1-1-1-1-11
χ31111111111111111111111111111-1-11111-1-111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-11111111111-1-1-1-1111-1-1-111-1-1-1-111-1-1-1-1-1-1111-1
χ5111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-1-1-1-1-1-1-111-1-111111-1
χ7111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11-1-1-111-1-1-1-111-1-11111-1-1-11
χ911111111111111-1-1-1-111111111111111-1-111-1-1-1-1-1-1-1-1111111-11-11-1-111-1-111-1-111-1-111-1-1
χ1011111111111111-1-1-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-111-1-1-1-11111-1-11-1
χ1111111111111111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111-11-11111-1-1-1-111-1-1-1-1-1-111
χ1211111111111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1111111-1-11111-11
χ1311111111111111-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-111-1-111
χ1411111111111111-1-1-1-1111111-1-1-1-111-1-111-1-1-1-1-1-111111111-1-111-1111-1-111-1-1-1-1-1-1-1-111-11
χ1511111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11-11-11111-1-1-1-111111111-1-1
χ1611111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11-1-1-1-1-111111111-1-1-1-11-1
χ172222222-1222-1-1-12222-1-1-1-1-1-1000022222222-1-1-1-100000000002-12-1-1-1-1-1-1-1-1-1-1-100000000
χ182222222-1222-1-1-12222-1-1-1-1-1-1000022-2-2-2-2-2-2-1-1-1-10000000000-2-12-111111111-1-100000000
χ192222222-1222-1-1-12222-1-1-1-1-1-10000-2-22222-2-2-1-1-1-10000000000-21-2111-1-1-1-1111100000000
χ202222222-1222-1-1-12222-1-1-1-1-1-10000-2-2-2-2-2-222-1-1-1-1000000000021-21-1-11111-1-11100000000
χ212222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-100002222-2-22211110000000000-2-1-2-111-1-111-1-11100000000
χ222222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-1000022-2-222-2-2111100000000002-1-2-1-1-111-1-1111100000000
χ232222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-10000-2-222-2-2-2-2111100000000002121-1-1-1-11111-1-100000000
χ242222222-1222-1-1-1-2-2-2-2-1-1-1-1-1-10000-2-2-2-2222211110000000000-21211111-1-1-1-1-1-100000000
χ252222-22-22-22-22220000-2-222-2-22222002-200000000000022-2-2-2-20000002-200000000000000
χ262222-22-22-22-22220000-2-222-2-2222200-22000000000000-2-222-2-2000000-2200000000000000
χ272222-22-22-22-22220000-2-222-2-2-2-2-2-2002-2000000000000-2-222220000002-200000000000000
χ282222-22-22-22-22220000-2-222-2-2-2-2-2-200-2200000000000022-2-222000000-2200000000000000
χ2922-2-22222-2-2-22-2-20000222-2-2-2000000002-20000002i2i−2i−2i2i−2i2i−2i00000000002-2000000000000
χ3022-2-22222-2-2-22-2-20000222-2-2-2000000002-2000000−2i−2i2i2i−2i2i−2i2i00000000002-2000000000000
χ3122-2-22222-2-2-22-2-20000222-2-2-200000000-220000002i2i−2i−2i−2i2i−2i2i0000000000-22000000000000
χ3222-2-22222-2-2-22-2-20000222-2-2-200000000-22000000−2i−2i2i2i2i−2i2i−2i0000000000-22000000000000
χ3322-2-22-2-2222-22-2-200002-2-222-222-2-22-20000000000000000002-2020-200000000002-2000000
χ3422-2-22-2-2222-22-2-200002-2-222-222-2-2-220000000000000000002-20-2020000000000-22000000
χ3522-2-22-2-2222-22-2-200002-2-222-2-2-2222-2000000000000000000-22020-20000000000-22000000
χ3622-2-22-2-2222-22-2-200002-2-222-2-2-222-22000000000000000000-220-20200000000002-2000000
χ3722-2-2-22-222-222-2-222-2-2-2-22-22200000000000022-2-200002i−2i−2i2i0000000000000000002i−2i0000
χ3822-2-2-22-222-222-2-222-2-2-2-22-22200000000000022-2-20000−2i2i2i−2i000000000000000000−2i2i0000
χ3922-2-2-22-222-222-2-2-2-222-2-22-222000000000000-2-22200002i−2i−2i2i000000000000000000−2i2i0000
χ4022-2-2-22-222-222-2-2-2-222-2-22-222000000000000-2-2220000−2i2i2i−2i0000000000000000002i−2i0000
χ4122-2-2-2-222-2222-2-20000-22-22-2222-2-20000002i−2i000000000000-2200000000002i−2i0000002i−2i00
χ4222-2-2-2-222-2222-2-20000-22-22-2222-2-2000000−2i2i000000000000-220000000000−2i2i000000−2i2i00
χ4322-2-2-2-222-2222-2-20000-22-22-22-2-2220000002i−2i0000000000002-200000000002i−2i000000−2i2i00
χ4422-2-2-2-222-2222-2-20000-22-22-22-2-222000000−2i2i0000000000002-20000000000−2i2i0000002i−2i00
χ4544444-4-44-4-4444400004-4-4-4-44000000000000000000000000000000000000000000000000
χ4644444-4-4-2-4-44-2-2-20000-22222-200000000000000000000000000000023−230000000000000000
χ4744444-4-4-2-4-44-2-2-20000-22222-2000000000000000000000000000000−23230000000000000000
χ484444-44-4-2-44-4-2-2-2000022-2-2220000004-4000000000000000000000000-2200000000000000
χ494444-44-4-2-44-4-2-2-2000022-2-222000000-440000000000000000000000002-200000000000000
χ504444-4-4444-4-44440000-44-4-44-4000000000000000000000000000000000000000000000000
χ514444-4-44-24-4-4-2-2-200002-222-220000000000000000000000000000000000000023−2300000000
χ524444-4-44-24-4-4-2-2-200002-222-2200000000000000000000000000000000000000−232300000000
χ5344-4-4444-2-4-4-4-2220000-2-2-2222000000004-4000000000000000000000000-22000000000000
χ5444-4-4444-2-4-4-4-2220000-2-2-222200000000-440000000000000000000000002-2000000000000
χ5544-4-44-4-4-244-4-2220000-222-2-2200004-4000000000000000000000-202000000000000000000
χ5644-4-44-4-4-244-4-2220000-222-2-220000-4400000000000000000000020-2000000000000000000
χ5744-4-4-44-4-24-44-22244-4-422-22-2-2000000000000-2-22200000000000000000000000000000000
χ5844-4-4-44-4-24-44-222-4-44422-22-2-200000000000022-2-200000000000000000000000000000000
χ5944-4-4-4-44-2-444-22200002-22-22-200000000004i−4i000000000000000000000000−2i2i0000000000
χ6044-4-4-4-44-2-444-22200002-22-22-20000000000−4i4i0000000000000000000000002i−2i0000000000
χ614-44i−4i0004000-44i−4i2-22i−2i00000022−22−2i22i2000000002-22i−2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000
χ624-44i−4i0004000-44i−4i2-22i−2i000000−22222i2−2i2000000002-22i−2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000
χ634-44i−4i0004000-44i−4i-22−2i2i00000022−22−2i22i200000000-22−2i2i−2ζ7−2ζ232ζ7+2ζ232ζ5+2ζ13−2ζ5−2ζ130000000000000000000000000000
χ644-44i−4i0004000-44i−4i-22−2i2i000000−22222i2−2i200000000-22−2i2i2ζ7+2ζ23−2ζ7−2ζ23−2ζ5−2ζ132ζ5+2ζ130000000000000000000000000000
χ654-4−4i4i0004000-4−4i4i2-2−2i2i00000022−222i2−2i2000000002-2−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000
χ664-4−4i4i0004000-4−4i4i2-2−2i2i000000−2222−2i22i2000000002-2−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000
χ674-4−4i4i0004000-4−4i4i-222i−2i00000022−222i2−2i200000000-222i−2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000000000000000000000000000
χ684-4−4i4i0004000-4−4i4i-222i−2i000000−2222−2i22i200000000-222i−2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000000000000000000000000000
χ698-88i−8i000-40004−4i4i4-44i−4i000000000000000000-22−2i2i00000000000000000000000000000000
χ708-88i−8i000-40004−4i4i-44−4i4i0000000000000000002-22i−2i00000000000000000000000000000000
χ718-8−8i8i000-400044i−4i4-4−4i4i000000000000000000-222i−2i00000000000000000000000000000000
χ728-8−8i8i000-400044i−4i-444i−4i0000000000000000002-2−2i2i00000000000000000000000000000000

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