Finite Group Databasebeta

← Group #134875

Character table — Group #134875

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222222222224444888888888888888888888888883232323232323232
order12222244448888888844442222444444448888888888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-11-111-1111-1-1-1-1-1-1-1-1-1-111-1-11111ii−i−iii−i−i
χ6111111111111111111-1-1-1-11-111-1111-1-1-1-1-1-1-1-1-1-111-1-11111−i−iii−i−iii
χ7111111111111111111-1-1-1-11-1-1-1-11-1-11111-1-1111111-1-1-1-1-1-1ii−i−i−i−iii
χ8111111111111111111-1-1-1-11-1-1-1-11-1-11111-1-1111111-1-1-1-1-1-1−i−iiiii−i−i
χ91111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11-1
χ101111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-11
χ111111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111111-11-1-11-11
χ121111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-11-111-11-1
χ131111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1111-1-1-1-1111111-1-111-1-1-1-1i−i−iii−i−ii
χ141111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1111-1-1-1-1111111-1-111-1-1-1-1−iii−i−iii−i
χ151111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1111111-1-1-1-1-1-1111111i−i−ii−iii−i
χ161111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1111111-1-1-1-1-1-1111111−iii−ii−i−ii
χ1722222222222222222222-2-2-2-2002-2000000220000-2-2-2-2000000000000
χ18222222222222222222-2-222-2200-2-2000000-2-20000-2-222000000000000
χ192222222222-2-2-2-2-2-2-2-222-2-2-2-2002-2000000-2-200002222000000000000
χ202222222222-2-2-2-2-2-2-2-2-2-222-2200-2-200000022000022-2-2000000000000
χ21222222-2-2-2-2000000002222-2-222-22-2-222-2-20000000000000000000000
χ22222222-2-2-2-2000000002222-2-2-2-2-2222-2-2220000000000000000000000
χ23222222-2-2-2-20000000022-2-22200-2-2000000002i2i−2i−2i00002i2i−2i−2i00000000
χ24222222-2-2-2-20000000022-2-22200-2-200000000−2i−2i2i2i0000−2i−2i2i2i00000000
χ25222222-2-2-2-200000000-2-2222-2002-2000000002i2i−2i−2i0000−2i−2i2i2i00000000
χ26222222-2-2-2-200000000-2-2222-2002-200000000−2i−2i2i2i00002i2i−2i−2i00000000
χ27222222-2-2-2-200000000-2-2-2-2-222222-2-2-2-2220000000000000000000000
χ28222222-2-2-2-200000000-2-2-2-2-22-2-2222222-2-20000000000000000000000
χ294444-4-444-4-40000000000000000000000000000004i−4i00000000000000
χ304444-4-444-4-4000000000000000000000000000000−4i4i00000000000000
χ314444-4-4-4-4444444-4-4-4-400000000000000000000000000000000000000
χ324444-4-4-4-444-4-4-4-4444400000000000000000000000000000000000000
χ3344-4-4004i−4i002i22i2−2i2−2i22222−22−220000000000002i−2i2-2002ζ−2ζ2ζ3−2ζ30000000000000000
χ3444-4-4004i−4i002i22i2−2i2−2i22222−22−22000000000000−2i2i-2200−2ζ2ζ−2ζ32ζ30000000000000000
χ3544-4-4004i−4i00−2i2−2i22i22i2−22−2222220000000000002i−2i2-200−2ζ2ζ−2ζ32ζ30000000000000000
χ3644-4-4004i−4i00−2i2−2i22i22i2−22−222222000000000000−2i2i-22002ζ−2ζ2ζ3−2ζ30000000000000000
χ3744-4-400−4i4i002i22i2−2i2−2i2−22−2222220000000000002i−2i-2200−2ζ32ζ3−2ζ2ζ0000000000000000
χ3844-4-400−4i4i002i22i2−2i2−2i2−22−222222000000000000−2i2i2-2002ζ3−2ζ32ζ−2ζ0000000000000000
χ3944-4-400−4i4i00−2i2−2i22i22i22222−22−220000000000002i−2i-22002ζ3−2ζ32ζ−2ζ0000000000000000
χ4044-4-400−4i4i00−2i2−2i22i22i22222−22−22000000000000−2i2i2-200−2ζ32ζ3−2ζ2ζ0000000000000000
χ414-44-44-400002i2−2i22i2−2i22i2−2i22i2−2i2004i−4i0000000000000000000022−22000000000000
χ424-44-44-400002i2−2i22i2−2i22i2−2i22i2−2i200−4i4i00000000000000000000−2222000000000000
χ434-44-44-40000−2i22i2−2i22i2−2i22i2−2i22i2004i−4i00000000000000000000−2222000000000000
χ444-44-44-40000−2i22i2−2i22i2−2i22i2−2i22i200−4i4i0000000000000000000022−22000000000000
χ454-44-4-4400002i2−2i22i2−2i2−2i22i2−2i22i24-4000000000000002i2−2i200000000000000000000
χ464-44-4-4400002i2−2i22i2−2i2−2i22i2−2i22i2-4400000000000000−2i22i200000000000000000000
χ474-44-4-440000−2i22i2−2i22i22i2−2i22i2−2i24-400000000000000−2i22i200000000000000000000
χ484-44-4-440000−2i22i2−2i22i22i2−2i22i2−2i2-44000000000000002i2−2i200000000000000000000
χ494-4-4400004-400004i−4i−4i4i0000002-2002-2000000000000002i−2i2i−2i00000000
χ504-4-4400004-400004i−4i−4i4i000000-2200-2200000000000000−2i2i−2i2i00000000
χ514-4-4400004-40000−4i4i4i−4i0000002-2002-200000000000000−2i2i−2i2i00000000
χ524-4-4400004-40000−4i4i4i−4i000000-2200-22000000000000002i−2i2i−2i00000000
χ534-4-440000-444-4-4400000000002-200-22000000000000002-2-2200000000
χ544-4-440000-444-4-440000000000-22002-200000000000000-222-200000000
χ554-4-440000-44-444-400000000002-200-2200000000000000-222-200000000
χ564-4-440000-44-444-40000000000-22002-2000000000000002-2-2200000000

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