Finite Group Databasebeta

← Group #94271

Character table — Group #94271

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111222222444444444444444444444444444488881616161616163232323232323232
order12222244444444444444448888888888888888444424888888888888
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
χ51111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-1-1
χ61111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ9111111-1-1-1-1111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11-1ii−i−i1-1i−i1-1i−i
χ10111111-1-1-1-1111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11-1ii−i−i-11−ii-11−ii
χ11111111-1-1-1-1111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-11−i−iiii−i-11−ii1-1
χ12111111-1-1-1-1111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111-11−i−iii−ii1-1i−i-11
χ13111111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11-1−i−iii1-1−ii1-1−ii
χ14111111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11-1−i−iii-11i−i-11i−i
χ15111111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-11ii−i−ii−i1-1−ii-11
χ16111111-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111-11ii−i−i−ii-11i−i1-1
χ17222222222222-2-2-2-2-2-2-2-222000000000000000022-2-2-22000000000000
χ18222222222222-2-2-2-2-2-2-2-2220000000000000000-2-2222-2000000000000
χ19222222-2-2-2-222-2-2-2-22222-2-200000000000000002222-2-2000000000000
χ20222222-2-2-2-222-2-2-2-22222-2-20000000000000000-2-2-2-222000000000000
χ2122-2-22-200002-2000022-2-200i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22i−2i2i−2i002−22−200000000
χ2222-2-22-200002-2000022-2-200i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2−2i2i−2i2i00−22−2200000000
χ2322-2-22-200002-2000022-2-200−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22i−2i2i−2i00−22−2200000000
χ2422-2-22-200002-2000022-2-200−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−2i2i−2i2i002−22−200000000
χ2522-2-22-200002-20000-2-222002222−2−2−2−2−2−2−2−222222i−2i−2i2i00−i2i2i2−i200000000
χ2622-2-22-200002-20000-2-222002222−2−2−2−2−2−2−2−22222−2i2i2i−2i00i2−i2−i2i200000000
χ2722-2-22-200002-20000-2-22200−2−2−2−222222222−2−2−2−22i−2i−2i2i00i2−i2−i2i200000000
χ2822-2-22-200002-20000-2-22200−2−2−2−222222222−2−2−2−2−2i2i2i−2i00−i2i2i2−i200000000
χ294444444444-4-400000000-4-40000000000000000000000000000000000
χ30444444-4-4-4-4-4-400000000440000000000000000000000000000000000
χ314444-4-444-4-40000000000002i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i000000000000000000
χ324444-4-444-4-4000000000000−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i000000000000000000
χ334444-4-4-4-44400000000000022-2-222-2-2-2-222-2-222000000000000000000
χ344444-4-4-4-444000000000000-2-222-2-22222-2-222-2-2000000000000000000
χ3544-4-44-40000-444i4i−4i−4i0000000000000000000000000000000000000000
χ3644-4-44-40000-44−4i−4i4i4i0000000000000000000000000000000000000000
χ3744-4-4-44000000000000004i−4i2ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ3000000000000000000
χ3844-4-4-44000000000000004i−4i−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3000000000000000000
χ3944-4-4-4400000000000000−4i4i2ζ32ζ3−2ζ3−2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ2ζ2ζ−2ζ−2ζ000000000000000000
χ4044-4-4-4400000000000000−4i4i−2ζ3−2ζ32ζ32ζ32ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ−2ζ−2ζ2ζ2ζ000000000000000000
χ414-44-400004i−4i002-22-22i−2i2i−2i00002+2i−2−2i002+2i−2−2i2−2i−2+2i002−2i−2+2i00000000000000000000
χ424-44-400004i−4i002-22-22i−2i2i−2i0000−2−2i2+2i00−2−2i2+2i−2+2i2−2i00−2+2i2−2i00000000000000000000
χ434-44-400004i−4i00-22-22−2i2i−2i2i002+2i−2−2i002+2i−2−2i00002−2i−2+2i002−2i−2+2i000000000000000000
χ444-44-400004i−4i00-22-22−2i2i−2i2i00−2−2i2+2i00−2−2i2+2i0000−2+2i2−2i00−2+2i2−2i000000000000000000
χ454-44-40000−4i4i002-22-2−2i2i−2i2i00002−2i−2+2i002−2i−2+2i2+2i−2−2i002+2i−2−2i00000000000000000000
χ464-44-40000−4i4i002-22-2−2i2i−2i2i0000−2+2i2−2i00−2+2i2−2i−2−2i2+2i00−2−2i2+2i00000000000000000000
χ474-44-40000−4i4i00-22-222i−2i2i−2i002−2i−2+2i002−2i−2+2i00002+2i−2−2i002+2i−2−2i000000000000000000
χ484-44-40000−4i4i00-22-222i−2i2i−2i00−2+2i2−2i00−2+2i2−2i0000−2−2i2+2i00−2−2i2+2i000000000000000000
χ494-4-44004-400002i−2i−2i2i2i−2i−2i2i002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000
χ504-4-44004-400002i−2i−2i2i2i−2i−2i2i00−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000
χ514-4-44004-40000−2i2i2i−2i−2i2i2i−2i002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000
χ524-4-44004-40000−2i2i2i−2i−2i2i2i−2i00−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000
χ534-4-4400-4400002i−2i−2i2i−2i2i2i−2i002ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ000000000000000000
χ544-4-4400-4400002i−2i−2i2i−2i2i2i−2i00−2ζ32ζ32ζ−2ζ2ζ3−2ζ3−2ζ2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ32ζ−2ζ000000000000000000
χ554-4-4400-440000−2i2i2i−2i2i−2i−2i2i002ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ3000000000000000000
χ564-4-4400-440000−2i2i2i−2i2i−2i−2i2i00−2ζ2ζ2ζ3−2ζ32ζ−2ζ−2ζ32ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ2ζ3−2ζ3000000000000000000

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