Finite Group Databasebeta

← Group #143902

Character table — Group #143902

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222222224444888888888888888888888888883232323232323232
order122222444488888888444422448888881616161616161616161616161616161624448888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ51111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-111
χ61111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ9222222222222222222-2-2-2-20000-2-20000000000002222-2-2-2-200000000
χ10222222222222222222-2-2-2-20000-2-2000000000000-2-2-2-2222200000000
χ112222222222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2000000000000000000000000
χ122222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222000000000000000000000000
χ132222222222-2-2-2-2-2-2-2-2-2-2-2-200002200002i2i2i2i−2i−2i−2i−2i0000000000000000
χ142222222222-2-2-2-2-2-2-2-2-2-2-2-20000220000−2i−2i−2i−2i2i2i2i2i0000000000000000
χ15222222-2-2-2-20000000022-2-20000002i2i−2i−2ii2i2−i2−i2i2i2−i2−i222−2−222−2−200000000
χ16222222-2-2-2-20000000022-2-20000002i2i−2i−2i−i2−i2i2i2−i2−i2i2i2−2−222−2−22200000000
χ17222222-2-2-2-20000000022-2-2000000−2i−2i2i2ii2i2−i2−i2i2i2−i2−i2−2−222−2−22200000000
χ18222222-2-2-2-20000000022-2-2000000−2i−2i2i2i−i2−i2i2i2−i2−i2i2i222−2−222−2−200000000
χ19222222-2-2-2-200000000-2-22222-2-200000022−2−2−2−22222−2−2−2−22200000000
χ20222222-2-2-2-200000000-2-22222-2-2000000−2−22222−2−2−2−22222−2−200000000
χ21222222-2-2-2-200000000-2-222-2-22200000022−2−2−2−222−2−22222−2−200000000
χ22222222-2-2-2-200000000-2-222-2-222000000−2−22222−2−222−2−2−2−22200000000
χ232222-2-2-2-22222-2-2-2-2222-22-200002-200000000000000000000002-20000
χ242222-2-2-2-22222-2-2-2-2222-22-200002-20000000000000000000000-220000
χ252222-2-2-2-22222-2-2-2-222-22-220000-22000000000000000000002-2000000
χ262222-2-2-2-22222-2-2-2-222-22-220000-2200000000000000000000-22000000
χ272222-2-2-2-222-2-22222-2-22-22-20000-22000000000000000000000000002-2
χ282222-2-2-2-222-2-22222-2-22-22-20000-2200000000000000000000000000-22
χ292222-2-2-2-222-2-22222-2-2-22-2200002-20000000000000000000000002-200
χ302222-2-2-2-222-2-22222-2-2-22-2200002-2000000000000000000000000-2200
χ314444-4-444-4-4000000004-4-440000000000000000000000000000000000
χ324444-4-444-4-400000000-444-40000000000000000000000000000000000
χ3344-4-4004i−4i0022−222i22i2−2i2−2i222−2200002-22i−2i002ζ2−2ζ22ζ6−2ζ6000000000000000000000000
χ3444-4-4004i−4i0022−222i22i2−2i2−2i222−220000-22−2i2i00−2ζ22ζ2−2ζ62ζ6000000000000000000000000
χ3544-4-4004i−4i00−2222−2i2−2i22i22i2−222200002-22i−2i00−2ζ22ζ2−2ζ62ζ6000000000000000000000000
χ3644-4-4004i−4i00−2222−2i2−2i22i22i2−22220000-22−2i2i002ζ2−2ζ22ζ6−2ζ6000000000000000000000000
χ3744-4-400−4i4i0022−22−2i2−2i22i22i222−2200002-2−2i2i00−2ζ62ζ6−2ζ22ζ2000000000000000000000000
χ3844-4-400−4i4i0022−22−2i2−2i22i22i222−220000-222i−2i002ζ6−2ζ62ζ2−2ζ2000000000000000000000000
χ3944-4-400−4i4i00−22222i22i2−2i2−2i2−222200002-2−2i2i002ζ6−2ζ62ζ2−2ζ2000000000000000000000000
χ4044-4-400−4i4i00−22222i22i2−2i2−2i2−22220000-222i−2i00−2ζ62ζ6−2ζ22ζ2000000000000000000000000
χ414-44-44-4000022−2222−2222−22−2222000000000000000000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ700000000
χ424-44-44-4000022−2222−2222−22−222200000000000000000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ700000000
χ434-44-44-40000−2222−2222−222222−22000000000000000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ500000000
χ444-44-44-40000−2222−2222−222222−2200000000000000000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ500000000
χ454-44-4-44000022−22−2222−2222−222200000000000000000000002ζ3+2ζ5−2ζ3−2ζ52ζ+2ζ7−2ζ−2ζ7000000000000
χ464-44-4-44000022−22−2222−2222−22220000000000000000000000−2ζ3−2ζ52ζ3+2ζ5−2ζ−2ζ72ζ+2ζ7000000000000
χ474-44-4-440000−222222−2222−2222−2200000000000000000000002ζ+2ζ7−2ζ−2ζ7−2ζ3−2ζ52ζ3+2ζ5000000000000
χ484-44-4-440000−222222−2222−2222−220000000000000000000000−2ζ−2ζ72ζ+2ζ72ζ3+2ζ5−2ζ3−2ζ5000000000000
χ494-4-4400004-4004i−4i−4i4i00000000000000002ζ2−2ζ22ζ2−2ζ22ζ6−2ζ62ζ6−2ζ60000000000000000
χ504-4-4400004-4004i−4i−4i4i0000000000000000−2ζ22ζ2−2ζ22ζ2−2ζ62ζ6−2ζ62ζ60000000000000000
χ514-4-4400004-400−4i4i4i−4i00000000000000002ζ6−2ζ62ζ6−2ζ62ζ2−2ζ22ζ2−2ζ20000000000000000
χ524-4-4400004-400−4i4i4i−4i0000000000000000−2ζ62ζ6−2ζ62ζ6−2ζ22ζ2−2ζ22ζ20000000000000000
χ534-4-440000-44440000-4-4000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ544-4-440000-44440000-4-400000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ554-4-440000-44-4-4000044000000000000002-2-222-2-220000000000000000
χ564-4-440000-44-4-400004400000000000000-222-2-222-20000000000000000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.