Finite Group Databasebeta

← Group #145464

Character table — Group #145464

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444444444444444444441616161616161616161616161616161632323232
order1222224444444488884488888888888888888888882244888816161616161616164488
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ922222222222222-2-2-2-222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-200000000000000000000
χ1022222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000
χ112222222-222-2-22-22222-2-222-2-2-2-2000000000000000022-2-20000000000000000
χ122222222-222-2-22-22222-2-222-2-2-2-20000000000000000-2-2220000000000000000
χ132222222-222-2-22-2-2-2-2-2-2-2-2-22222000000000000000000002i2i−2i−2i000000000000
χ142222222-222-2-22-2-2-2-2-2-2-2-2-2222200000000000000000000−2i−2i2i2i000000000000
χ15222222-2-2-2-2-2-2-2-20000220000002i2i2i2i−2i−2i−2i−2i000000000000000022−2−2i2i2−i2−i20000
χ16222222-2-2-2-2-2-2-2-20000220000002i2i2i2i−2i−2i−2i−2i0000000000000000−2−222−i2−i2i2i20000
χ17222222-2-2-2-2-2-2-2-2000022000000−2i−2i−2i−2i2i2i2i2i000000000000000022−2−2−i2−i2i2i20000
χ18222222-2-2-2-2-2-2-2-2000022000000−2i−2i−2i−2i2i2i2i2i0000000000000000−2−222i2i2−i2−i20000
χ192222-2-222-2-2-2-2220000-22000000000000002222-2-2-2-2000000002−22−22−22−20000
χ202222-2-222-2-2-2-2220000-22000000000000002222-2-2-2-200000000−22−22−22−220000
χ212222-2-222-2-2-2-2220000-2200000000000000-2-2-2-22222000000002−22−2−22−220000
χ222222-2-222-2-2-2-2220000-2200000000000000-2-2-2-2222200000000−22−222−22−20000
χ232222-2-2-2222-2-2-2222222-2-2-222-2-2000000000000000000000000000000002-200
χ242222-2-2-2222-2-2-2222222-2-2-222-2-200000000000000000000000000000000-2200
χ252222-2-2-2222-2-2-22-2-2-2-22-222-2-22200000000000000000000000000000000002i−2i
χ262222-2-2-2222-2-2-22-2-2-2-22-222-2-2220000000000000000000000000000000000−2i2i
χ272222-2-2-2-22222-2-22222-22-2-2-2-2220000000000000000000000002-2-2200000000
χ282222-2-2-2-22222-2-22222-22-2-2-2-222000000000000000000000000-222-200000000
χ292222-2-2-2-22222-2-2-2-2-2-2-222222-2-200000000000000000000000000002i−2i−2i2i0000
χ302222-2-2-2-22222-2-2-2-2-2-2-222222-2-20000000000000000000000000000−2i2i2i−2i0000
χ3122-2-22-2202-200-2022-2-2002-2000022−2−222−2−222−2−222−2−22-2002−22−2000000000000
χ3222-2-22-2202-200-2022-2-2002-2000022−2−222−2−222−2−222−2−2-2200−22−22000000000000
χ3322-2-22-2202-200-2022-2-2002-20000−2−222−2−222−2−222−2−2222-200−22−22000000000000
χ3422-2-22-2202-200-2022-2-2002-20000−2−222−2−222−2−222−2−222-22002−22−2000000000000
χ3522-2-22-2202-200-20-2-22200-22000022−2−222−2−2−2−222−2−222002i−2ii2−i2−i2i2000000000000
χ3622-2-22-2202-200-20-2-22200-22000022−2−222−2−2−2−222−2−22200−2i2i−i2i2i2−i2000000000000
χ3722-2-22-2202-200-20-2-22200-220000−2−222−2−22222−2−222−2−2002i−2i−i2i2i2−i2000000000000
χ3822-2-22-2202-200-20-2-22200-220000−2−222−2−22222−2−222−2−200−2i2ii2−i2−i2i2000000000000
χ39444444-44-4-444-440000-4-4000000000000000000000000000000000000000000
χ404444-4-44-4-4-4444-400004-4000000000000000000000000000000000000000000
χ4144-4-44-4-40-4400400000000000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000
χ4244-4-44-4-40-440040000000000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000
χ4344-4-4-4440-4400-40000000000000000000002222−22−22−22−22222200000000000000000000
χ4444-4-4-4440-4400-4000000000000000000000−22−2222222222−22−2200000000000000000000
χ4544-4-4-44-404-4004044-4-400-440000000000000000000000000000000000000000
χ4644-4-4-44-404-40040-4-444004-40000000000000000000000000000000000000000
χ474-44-40000004i−4i0022−2222−220000002i2−2i22ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ32-22-22i−2i2i−2i00000000000000000000
χ484-44-40000004i−4i0022−2222−220000002i2−2i2−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3-22-22−2i2i−2i2i00000000000000000000
χ494-44-40000004i−4i00−2222−2222000000−2i22i22ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3-22-22−2i2i−2i2i00000000000000000000
χ504-44-40000004i−4i00−2222−2222000000−2i22i2−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ32-22-22i−2i2i−2i00000000000000000000
χ514-44-4000000−4i4i0022−2222−22000000−2i22i22ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ-22-222i−2i2i−2i00000000000000000000
χ524-44-4000000−4i4i0022−2222−22000000−2i22i2−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ2-22-2−2i2i−2i2i00000000000000000000
χ534-44-4000000−4i4i00−2222−22220000002i2−2i22ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ2-22-2−2i2i−2i2i00000000000000000000
χ544-44-4000000−4i4i00−2222−22220000002i2−2i2−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ-22-222i−2i2i−2i00000000000000000000
χ554-4-44000400000-422−22−2222000022−22002i−2i−2i2i2i−2i−2i2i00002i2−2i2−2i22i200000000000000000000
χ564-4-44000400000-422−22−2222000022−2200−2i2i2i−2i−2i2i2i−2i0000−2i22i22i2−2i200000000000000000000
χ574-4-44000400000-4−222222−220000−2222002i−2i−2i2i2i−2i−2i2i0000−2i22i22i2−2i200000000000000000000
χ584-4-44000400000-4−222222−220000−222200−2i2i2i−2i−2i2i2i−2i00002i2−2i2−2i22i200000000000000000000
χ594-4-44000-400000422−22−22220000−2222002-2-22-222-222−22−2222000000000000000000000000
χ604-4-44000-400000422−22−22220000−222200-222-22-2-22−222222−22000000000000000000000000
χ614-4-44000-4000004−222222−22000022−22002-2-22-222-2−222222−22000000000000000000000000
χ624-4-44000-4000004−222222−22000022−2200-222-22-2-2222−22−2222000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.