Finite Group Databasebeta

← Group #149819

Character table — Group #149819

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444444444444444444488881616161616163232323232323232
order1244244444222444444444888888888888888888888888881616161616161616
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i
χ911111-1-1-1-111-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-11-11-11-11-1
χ1011111-1-1-1-111-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-11-11-11-11
χ1111111-1-1-1-111-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ1211111-1-1-1-111-1-1-1-11111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ1311111-1-1-1-111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1111-1-111-1-11
χ1411111-1-1-1-111-1-1-1-11111-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-111-111-1-111-1
χ1511111-1-1-1-111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1i−i−ii−iii−i
χ1611111-1-1-1-111-1-1-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1−iii−ii−i−ii
χ1722222222222-2-2-2-2-2-2-2-2222000000000000000022-2-2002-20000000000
χ1822222222222-2-2-2-2-2-2-2-22220000000000000000-2-22200-220000000000
χ1922222-2-2-2-2222222-2-2-2-2-2-22000000000000000022-2-200-220000000000
χ2022222-2-2-2-2222222-2-2-2-2-2-220000000000000000-2-222002-20000000000
χ2122-2-220000-2-2000022-2-2002000000002222-2-2-2-22i−2i2i−2i00002i−2i00000000
χ2222-2-220000-2-2000022-2-2002000000002222-2-2-2-2−2i2i−2i2i0000−2i2i00000000
χ2322-2-220000-2-2000022-2-200200000000-2-2-2-222222i−2i2i−2i0000−2i2i00000000
χ2422-2-220000-2-2000022-2-200200000000-2-2-2-22222−2i2i−2i2i00002i−2i00000000
χ2522-2-220000-2-20000-2-2220022222-2-2-2-2000000002i−2i−2i2i2i−2i000000000000
χ2622-2-220000-2-20000-2-2220022222-2-2-2-200000000−2i2i2i−2i−2i2i000000000000
χ2722-2-220000-2-20000-2-222002-2-2-2-22222000000002i−2i−2i2i−2i2i000000000000
χ2822-2-220000-2-20000-2-222002-2-2-2-2222200000000−2i2i2i−2i2i−2i000000000000
χ294444444444-400000000-4-4-40000000000000000000000000000000000
χ3044444-4-4-4-44-40000000044-40000000000000000000000000000000000
χ314444-40000-40000000004i−4i022-2-222-2-22i2i−2i−2i2i2i−2i−2i000000000000000000
χ324444-40000-40000000004i−4i0-2-222-2-222−2i−2i2i2i−2i−2i2i2i000000000000000000
χ334444-40000-4000000000−4i4i022-2-222-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000
χ344444-40000-4000000000−4i4i0-2-222-2-2222i2i−2i−2i2i2i−2i−2i000000000000000000
χ3544-4-440000-4444-4-4000000-40000000000000000000000000000000000
χ3644-4-440000-44-4-444000000-40000000000000000000000000000000000
χ3744-4-4-44i4i−4i−4i400000000000022-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000
χ3844-4-4-44i4i−4i−4i4000000000000-2-22222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000
χ3944-4-4-4−4i−4i4i4i400000000000022-2-2-2-222−2i−2i2i2i2i2i−2i−2i000000000000000000
χ4044-4-4-4−4i−4i4i4i4000000000000-2-22222-2-22i2i−2i−2i−2i−2i2i2i000000000000000000
χ414-44i−4i02+2i−2−2i2−2i−2+2i002-22i−2i2i−2i2-2000002i2−2i20022−222ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ000000000000000000
χ424-44i−4i02+2i−2−2i2−2i−2+2i002-22i−2i2i−2i2-200000−2i22i200−2222−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ000000000000000000
χ434-44i−4i02+2i−2−2i2−2i−2+2i00-22−2i2i−2i2i-220002i2−2i20022−22002ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ3000000000000000000
χ444-44i−4i02+2i−2−2i2−2i−2+2i00-22−2i2i−2i2i-22000−2i22i200−222200−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3000000000000000000
χ454-44i−4i0−2−2i2+2i−2+2i2−2i002-22i−2i−2i2i-220002i2−2i20022−2200−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3000000000000000000
χ464-44i−4i0−2−2i2+2i−2+2i2−2i002-22i−2i−2i2i-22000−2i22i200−2222002ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ3000000000000000000
χ474-44i−4i0−2−2i2+2i−2+2i2−2i00-22−2i2i2i−2i2-2000002i2−2i20022−22−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ000000000000000000
χ484-44i−4i0−2−2i2+2i−2+2i2−2i00-22−2i2i2i−2i2-200000−2i22i200−22222ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ000000000000000000
χ494-4−4i4i02−2i−2+2i2+2i−2−2i002-2−2i2i−2i2i2-2000002i2−2i200−22222ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ3000000000000000000
χ504-4−4i4i02−2i−2+2i2+2i−2−2i002-2−2i2i−2i2i2-200000−2i22i20022−22−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3000000000000000000
χ514-4−4i4i02−2i−2+2i2+2i−2−2i00-222i−2i2i−2i-220002i2−2i200−2222002ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ000000000000000000
χ524-4−4i4i02−2i−2+2i2+2i−2−2i00-222i−2i2i−2i-22000−2i22i20022−2200−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ000000000000000000
χ534-4−4i4i0−2+2i2−2i−2−2i2+2i002-2−2i2i2i−2i-220002i2−2i200−222200−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ000000000000000000
χ544-4−4i4i0−2+2i2−2i−2−2i2+2i002-2−2i2i2i−2i-22000−2i22i20022−22002ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ000000000000000000
χ554-4−4i4i0−2+2i2−2i−2−2i2+2i00-222i−2i−2i2i2-2000002i2−2i200−2222−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3000000000000000000
χ564-4−4i4i0−2+2i2−2i−2−2i2+2i00-222i−2i−2i2i2-200000−2i22i20022−222ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ3000000000000000000

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