Finite Group Databasebeta

← Group #9243

Character table — Group #9243

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43
size11112222222244444444444888888888888888816161616
order1222224444442244444888824888888888888882488
χ11111111111111111111111111111111111111111111
χ21111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-111-1-1
χ41111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-111
χ5111111111111-1-111-1-111111-1-111-1-1-1-111111111-1-1-1-1
χ6111111111111-1-111-1-111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111-1-111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ8111111111111-1-111-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ91111111-1-11-1-111-11-1-1-1ii−i−i1-1i−iii−i−i11-1-1ii−i−i1-1i−i
χ101111111-1-11-1-111-11-1-1-1ii−i−i1-1i−iii−i−i-1-111−i−iii-11−ii
χ111111111-1-11-1-111-11-1-1-1−i−iii1-1−ii−i−iii11-1-1−i−iii1-1−ii
χ121111111-1-11-1-111-11-1-1-1−i−iii1-1−ii−i−iii-1-111ii−i−i-11i−i
χ131111111-1-11-1-1-1-1-1111-1ii−i−i-11i−i−i−iii11-1-1ii−i−i-11−ii
χ141111111-1-11-1-1-1-1-1111-1ii−i−i-11i−i−i−iii-1-111−i−iii1-1i−i
χ151111111-1-11-1-1-1-1-1111-1−i−iii-11−iiii−i−i11-1-1−i−iii-11i−i
χ161111111-1-11-1-1-1-1-1111-1−i−iii-11−iiii−i−i-1-111ii−i−i1-1−ii
χ17222222-222-22200-2-200-2222200-2-20000000000000000
χ18222222-222-22200-2-200-2-2-2-2-200220000000000000000
χ19222222-2-2-2-2-2-2002-20022i2i−2i−2i00−2i2i0000000000000000
χ20222222-2-2-2-2-2-2002-2002−2i−2i2i2i002i−2i0000000000000000
χ212222-2-22222-2-222-2-2-2-220000-22000000000000000000
χ222222-2-22222-2-2-2-2-2-222200002-2000000000000000000
χ232222-2-22-2-2222222-222-20000-2-2000000000000000000
χ242222-2-22-2-2222-2-22-2-2-2-2000022000000000000000000
χ252222-2-2-222-2-2-2002200-2000000002i−2i2i−2i000000000000
χ262222-2-2-222-2-2-2002200-200000000−2i2i−2i2i000000000000
χ272222-2-2-2-2-2-22200-22002000000002-2-22000000000000
χ282222-2-2-2-2-2-22200-2200200000000-222-2000000000000
χ2922-2-22-202i−2i02i−2i00000002ζ−2ζ2ζ3−2ζ3000000002−2i2−i21+i−1−i1−i−1+i0000
χ3022-2-22-202i−2i02i−2i00000002ζ−2ζ2ζ3−2ζ300000000−22−i2i2−1−i1+i−1+i1−i0000
χ3122-2-22-202i−2i02i−2i0000000−2ζ2ζ−2ζ32ζ3000000002−2i2−i2−1−i1+i−1+i1−i0000
χ3222-2-22-202i−2i02i−2i0000000−2ζ2ζ−2ζ32ζ300000000−22−i2i21+i−1−i1−i−1+i0000
χ3322-2-22-20−2i2i0−2i2i00000002ζ3−2ζ32ζ−2ζ000000002−2−i2i2−1+i1−i−1−i1+i0000
χ3422-2-22-20−2i2i0−2i2i00000002ζ3−2ζ32ζ−2ζ00000000−22i2−i21−i−1+i1+i−1−i0000
χ3522-2-22-20−2i2i0−2i2i0000000−2ζ32ζ3−2ζ2ζ000000002−2−i2i21−i−1+i1+i−1−i0000
χ3622-2-22-20−2i2i0−2i2i0000000−2ζ32ζ3−2ζ2ζ00000000−22i2−i2−1+i1−i−1−i1+i0000
χ3744-4-4-4404i−4i0−4i4i0000000000000000000000000000000
χ3844-4-4-440−4i4i04i−4i0000000000000000000000000000000
χ394-44-400400-40000004i−4i0000000000000000000000000
χ404-44-400400-4000000−4i4i0000000000000000000000000
χ414-44-400-4004004-400000000000000000000000000000
χ424-44-400-400400-4400000000000000000000000000000
χ438-8-88000000000000000000000000000000000000000

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