Finite Group Databasebeta

← Group #152945

Character table — Group #152945

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size11112222444444488888888888888888161616161616161616323232323232
order12222244444444422444444488888888488888888444444
χ111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111-1-11-1-111-1-111111111-1iiii−i−i−i−i-1-1ii−i−i
χ6111111111111111-1-11-1-111-1-111111111-1−i−i−i−iiiii-1-1−i−iii
χ7111111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ8111111111111111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-11-11111111-1-1-1-1-1111111-1-1-1-1-111-1-111-1-11-11-11-1
χ10111111-1-11-11111111-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1111-1-11-11
χ11111111-1-11-11111111-1-1-1-1-111-1-1-1-11111-111-1-111-1-1-11-11-11
χ12111111-1-11-11111111-1-1-1-1-111-1-1-1-11111-1-1-111-1-111-111-11-1
χ13111111-1-11-111111-1-1-111-1-1-1-11111-1-1-1-11ii−i−i−i−iii-11i−i−ii
χ14111111-1-11-111111-1-1-111-1-1-1-11111-1-1-1-11−i−iiiii−i−i-11−iii−i
χ15111111-1-11-111111-1-1-111-1-1-1-1-1-1-1-111111ii−i−i−i−iii1-1−iii−i
χ16111111-1-11-111111-1-1-111-1-1-1-1-1-1-1-111111−i−iiiii−i−i1-1i−i−ii
χ172222222222-2-2-2-22222-2-2-2-2-2-200000000200000000000000
χ182222222222-2-2-2-22-2-2222-2-22200000000-200000000000000
χ19222222-2-22-2-2-2-2-2222-22222-2-200000000-200000000000000
χ20222222-2-22-2-2-2-2-22-2-2-2-2-2222200000000200000000000000
χ2122-2-2-2200-2022-2-222-2000002-2000000000002i−2i002i−2i000000
χ2222-2-2-2200-2022-2-222-2000002-200000000000−2i2i00−2i2i000000
χ2322-2-2-2200-2022-2-22-2200000-22000000000002-200-22000000
χ2422-2-2-2200-2022-2-22-2200000-2200000000000-22002-2000000
χ2522-2-2-2200-20-2-22222-200000-220000000002i−2i002i−2i00000000
χ2622-2-2-2200-20-2-22222-200000-22000000000−2i2i00−2i2i00000000
χ2722-2-2-2200-20-2-2222-22000002-20000000002-200-2200000000
χ2822-2-2-2200-20-2-2222-22000002-2000000000-22002-200000000
χ2944444444-440000-400-400000000000000000000000000000
χ30444444-4-4-4-40000-400400000000000000000000000000000
χ314444-4-4440-4000000000000002i2i−2i−2i2i2i−2i−2i000000000000000
χ324444-4-4440-400000000000000−2i−2i2i2i−2i−2i2i2i000000000000000
χ334444-4-4-4-404000000000000002i2i−2i−2i−2i−2i2i2i000000000000000
χ344444-4-4-4-40400000000000000−2i−2i2i2i2i2i−2i−2i000000000000000
χ3544-4-4-4400400000-40004i−4i000000000000000000000000000
χ3644-4-4-4400400000-4000−4i4i000000000000000000000000000
χ374-44-4004-4002i−2i2i−2i0000002i−2i002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000
χ384-44-4004-4002i−2i2i−2i0000002i−2i00−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000
χ394-44-4004-400−2i2i−2i2i000000−2i2i002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000
χ404-44-4004-400−2i2i−2i2i000000−2i2i00−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000
χ414-44-400-44002i−2i2i−2i000000−2i2i002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000
χ424-44-400-44002i−2i2i−2i000000−2i2i00−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000
χ434-44-400-4400−2i2i−2i2i0000002i−2i002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000
χ444-44-400-4400−2i2i−2i2i0000002i−2i00−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000
χ4588-8-88-800000000000000000000000000000000000000000
χ468-8-880000004i−4i−4i4i000000000000000000000000000000000
χ478-8-88000000−4i4i4i−4i000000000000000000000000000000000

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