Finite Group Databasebeta

← Group #150029

Character table — Group #150029

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222244444448888888881616161616161616161616161616161616161616163232
order12222244444444444444444444444888888888888888888
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1
χ51111111111-1-1-1-1111-1-11-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111-1-1-1-1111-1-11-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111-1-1-1-1111-1-11-1-1-1-1-1-11-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111-1-1-1-1111-1-11-1-1-1-1-1-11-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ9111111-1-11-11111111-1-1-1-1-1111-1-11-111-1-111-1-111-1-111-1-11-1
χ10111111-1-11-11111111-1-1-1-1-1111-1-11-1-1-111-1-111-1-111-1-1111-1
χ11111111-1-11-11111111-1-1-1-1-111-11-1-1111-1-111-1-1-1-111-1-111-11
χ12111111-1-11-11111111-1-1-1-1-111-11-1-11-1-111-1-11111-1-111-1-1-11
χ13111111-1-11-1-1-1-1-111111-111-1-11-1-11-1ii−i−i−i−iiiii−i−i−i−iii-11
χ14111111-1-11-1-1-1-1-111111-111-1-11-1-11-1−i−iiiii−i−i−i−iiiii−i−i-11
χ15111111-1-11-1-1-1-1-111111-111-1-1-11-1-11ii−i−i−i−iii−i−iiiii−i−i1-1
χ16111111-1-11-1-1-1-1-111111-111-1-1-11-1-11−i−iiiii−i−iii−i−i−i−iii1-1
χ17222222222222222-2-2-2-2222-2-200-200000000000000000000
χ182222222222-2-2-2-22-2-2222-2-22200-200000000000000000000
χ19222222-2-22-222222-2-222-2-2-2-2-200200000000000000000000
χ20222222-2-22-2-2-2-2-22-2-2-2-2-2222200200000000000000000000
χ2122-2-22-200-202i2i−2i−2i22-2000002i−2i0000000000000002ζ3−2ζ3002ζ−2ζ00
χ2222-2-22-200-202i2i−2i−2i22-2000002i−2i000000000000000−2ζ32ζ300−2ζ2ζ00
χ2322-2-22-200-202i2i−2i−2i2-2200000−2i2i00000000000002ζ3−2ζ3002ζ−2ζ0000
χ2422-2-22-200-202i2i−2i−2i2-2200000−2i2i0000000000000−2ζ32ζ300−2ζ2ζ0000
χ2522-2-22-200-20−2i−2i2i2i22-200000−2i2i0000000000000002ζ−2ζ002ζ3−2ζ300
χ2622-2-22-200-20−2i−2i2i2i22-200000−2i2i000000000000000−2ζ2ζ00−2ζ32ζ300
χ2722-2-22-200-20−2i−2i2i2i2-22000002i−2i00000000000002ζ−2ζ002ζ3−2ζ30000
χ2822-2-22-200-20−2i−2i2i2i2-22000002i−2i0000000000000−2ζ2ζ00−2ζ32ζ30000
χ2944444444-440000-40000-4000000000000000000000000000
χ30444444-4-4-4-40000-400004000000000000000000000000000
χ314444-4-4440-4000000000000002-20-22000000000000000000
χ324444-4-4440-400000000000000-2202-2000000000000000000
χ334444-4-4-4-40400000000000000220-2-2000000000000000000
χ344444-4-4-4-40400000000000000-2-2022000000000000000000
χ3544-4-44-400400000-4004-40000000000000000000000000000
χ3644-4-44-400400000-400-440000000000000000000000000000
χ374-4-44004i−4i002i−2i2i−2i0000002-200000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000
χ384-4-44004i−4i002i−2i2i−2i0000002-20000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000
χ394-4-44004i−4i00−2i2i−2i2i000000-2200000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000
χ404-4-44004i−4i00−2i2i−2i2i000000-220000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000
χ414-4-4400−4i4i002i−2i2i−2i000000-2200000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000
χ424-4-4400−4i4i002i−2i2i−2i000000-220000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000
χ434-4-4400−4i4i00−2i2i−2i2i0000002-200000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000
χ444-4-4400−4i4i00−2i2i−2i2i0000002-20000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000
χ4588-8-8-8800000000000000000000000000000000000000000
χ468-88-80000004-4-44000000000000000000000000000000000
χ478-88-8000000-444-4000000000000000000000000000000000

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