Finite Group Databasebeta

← Group #136262

Character table — Group #136262

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12224444224422444444444488888888888824444488888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111
χ6111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ7111111111111111111-1-1-1-111-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ8111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111-1-1-1-111-1-111-1-11-111-1-11-1ii−i−iii−i−iii−i−i1-111-1-1ii−i−ii−i11-1-1ii−i−i
χ101111-1-1-1-111-1-111-1-11-111-1-11-1ii−i−iii−i−iii−i−i1-1-1-111−i−iiii−i-1-111−i−iii
χ111111-1-1-1-111-1-111-1-11-111-1-11-1−i−iii−i−iii−i−iii1-111-1-1−i−iii−ii11-1-1−i−iii
χ121111-1-1-1-111-1-111-1-11-111-1-11-1−i−iii−i−iii−i−iii1-1-1-111ii−i−i−ii-1-111ii−i−i
χ131111-1-1-1-111-1-111-1-11-1-1-1111-1ii−i−i−i−iii−i−iii-1111-1-1−i−iiii−i-1-111ii−i−i
χ141111-1-1-1-111-1-111-1-11-1-1-1111-1ii−i−i−i−iii−i−iii-11-1-111ii−i−ii−i11-1-1−i−iii
χ151111-1-1-1-111-1-111-1-11-1-1-1111-1−i−iiiii−i−iii−i−i-1111-1-1ii−i−i−ii-1-111−i−iii
χ161111-1-1-1-111-1-111-1-11-1-1-1111-1−i−iiiii−i−iii−i−i-11-1-111−i−iii−ii11-1-1ii−i−i
χ172222222222222222-2-20000-2-200002222-2-2-2-200000000000000000000
χ182222222222222222-2-20000-2-20000-2-2-2-2222200000000000000000000
χ19222222222222-2-2-2-22-22222-22000000000000-2-2000000000000000000
χ20222222222222-2-2-2-22-2-2-2-2-2-2200000000000022000000000000000000
χ21222222222222-2-2-2-2-2200002-22222000000000000000000-2-200000000
χ22222222222222-2-2-2-2-2200002-2-2-2-2-20000000000000000002200000000
χ232222-2-2-2-222-2-222-2-2-220000-2200002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ242222-2-2-2-222-2-222-2-2-220000-220000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ252222-2-2-2-222-2-2-2-2222222-2-2-2-2000000000000-22000000000000000000
χ262222-2-2-2-222-2-2-2-22222-2-222-2-20000000000002-2000000000000000000
χ272222-2-2-2-222-2-2-2-222-2-20000222i2i−2i−2i000000000000000000−2i2i00000000
χ282222-2-2-2-222-2-2-2-222-2-2000022−2i−2i2i2i0000000000000000002i−2i00000000
χ292-2-2222-2-2-22-222-22-200000000000000002-22-2000000000000i2−i2i2−i2i2−i2i2−i2
χ302-2-2222-2-2-22-222-22-200000000000000002-22-2000000000000−i2i2−i2i2−i2i2−i2i2
χ312-2-2222-2-2-22-222-22-20000000000000000-22-22000000000000i2−i2i2−i2−i2i2−i2i2
χ322-2-2222-2-2-22-222-22-20000000000000000-22-22000000000000−i2i2−i2i2i2−i2i2−i2
χ332-2-22-2-222-222-22-2-2200000000000000002i−2i−2i2i000000000000i2−i2−i2i2−222−2
χ342-2-22-2-222-222-22-2-2200000000000000002i−2i−2i2i000000000000−i2i2i2−i22−2−22
χ352-2-22-2-222-222-22-2-220000000000000000−2i2i2i−2i000000000000i2−i2−i2i22−2−22
χ362-2-22-2-222-222-22-2-220000000000000000−2i2i2i−2i000000000000−i2i2i2−i2−222−2
χ3744444444-4-4-4-40000000000000000000000000000002-22-20000000000
χ3844444444-4-4-4-4000000000000000000000000000000-22-220000000000
χ394444-4-4-4-4-4-4440000000000000000000000000000002i−2i−2i2i0000000000
χ404444-4-4-4-4-4-444000000000000000000000000000000−2i2i2i−2i0000000000
χ4144-4-44i−4i4i−4i00000000002-22i−2i002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ4244-4-44i−4i4i−4i00000000002-22i−2i00−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ4344-4-44i−4i4i−4i0000000000-22−2i2i002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ4444-4-44i−4i4i−4i0000000000-22−2i2i00−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ4544-4-4−4i4i−4i4i00000000002-2−2i2i002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ4644-4-4−4i4i−4i4i00000000002-2−2i2i00−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ4744-4-4−4i4i−4i4i0000000000-222i−2i002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ4844-4-4−4i4i−4i4i0000000000-222i−2i00−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000000000000000
χ494-4-4444-4-44-44-4000000000000000000000000002-22-200000000000000
χ504-4-4444-4-44-44-400000000000000000000000000-22-2200000000000000
χ514-4-4444-4-4-44-44-44-440000000000000000000000000000000000000000
χ524-4-44-4-4444-4-44000000000000000000000000002-2-2200000000000000
χ534-4-44-4-4444-4-4400000000000000000000000000-222-200000000000000
χ544-4-44-4-444-444-4-444-40000000000000000000000000000000000000000
χ558-88-88i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000

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