Finite Group Databasebeta

← Group #9263

Character table — Group #9263

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43
size11112222222244444444444888888888888888816161616
order1222222244442448888888824444444888888884488
χ11111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1
χ41111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ5111111111111111-1-1-1-11111-1-1-1-11111-1-111-1-1-1-111-1-1
χ6111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111
χ7111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ9111111-1-1-1-1-1-1-111ii−i−iii−i−i1-11-1ii−i−ii−ii−i11-1-11-1i−i
χ10111111-1-1-1-1-1-1-111ii−i−iii−i−i1-11-1−i−iiii−ii−i-1-111-11−ii
χ11111111-1-1-1-1-1-1-111ii−i−i−i−iii-11-11ii−i−ii−i−ii11-1-1-11−ii
χ12111111-1-1-1-1-1-1-111ii−i−i−i−iii-11-11−i−iiii−i−ii-1-1111-1i−i
χ13111111-1-1-1-1-1-1-111−i−iiiii−i−i-11-11ii−i−i−iii−i-1-1111-1−ii
χ14111111-1-1-1-1-1-1-111−i−iiiii−i−i-11-11−i−iii−iii−i11-1-1-11i−i
χ15111111-1-1-1-1-1-1-111−i−iii−i−iii1-11-1ii−i−i−ii−ii-1-111-11i−i
χ16111111-1-1-1-1-1-1-111−i−iii−i−iii1-11-1−i−iii−ii−ii11-1-11-1−ii
χ1722222222-2-2-2-22-2-22i2i−2i−2i000000000000−2i2i0000000000
χ1822222222-2-2-2-22-2-2−2i−2i2i2i0000000000002i−2i0000000000
χ19222222-2-22222-2-2-22222000000000000-2-20000000000
χ20222222-2-22222-2-2-2-2-2-2-2000000000000220000000000
χ212222-2-22222-2-2-2-220000000022-2-20000000000000000
χ222222-2-22222-2-2-2-2200000000-2-2220000000000000000
χ232222-2-222-2-222-22-2000022220000000000-2-200000000
χ242222-2-222-2-222-22-20000-2-2-2-200000000002200000000
χ252222-2-2-2-222-2-222-200002i2i−2i−2i0000000000−2i2i00000000
χ262222-2-2-2-222-2-222-20000−2i−2i2i2i00000000002i−2i00000000
χ272222-2-2-2-2-2-2222-22000000002-2-220000000000000000
χ282222-2-2-2-2-2-2222-2200000000-222-20000000000000000
χ292-22-22-2002i−2i2i−2i0002ζ−2ζ2ζ3−2ζ3000000001+i−1−i1−i−1+i00002−2i2−i20000
χ302-22-22-2002i−2i2i−2i0002ζ−2ζ2ζ3−2ζ300000000−1−i1+i−1+i1−i0000−22−i2i20000
χ312-22-22-2002i−2i2i−2i000−2ζ2ζ−2ζ32ζ3000000001+i−1−i1−i−1+i0000−22−i2i20000
χ322-22-22-2002i−2i2i−2i000−2ζ2ζ−2ζ32ζ300000000−1−i1+i−1+i1−i00002−2i2−i20000
χ332-22-22-200−2i2i−2i2i0002ζ3−2ζ32ζ−2ζ000000001−i−1+i1+i−1−i0000−22i2−i20000
χ342-22-22-200−2i2i−2i2i0002ζ3−2ζ32ζ−2ζ00000000−1+i1−i−1−i1+i00002−2−i2i20000
χ352-22-22-200−2i2i−2i2i000−2ζ32ζ3−2ζ2ζ000000001−i−1+i1+i−1−i00002−2−i2i20000
χ362-22-22-200−2i2i−2i2i000−2ζ32ζ3−2ζ2ζ00000000−1+i1−i−1−i1+i0000−22i2−i20000
χ3744-4-4004-40000000000022−2222−2200000000000000000000
χ3844-4-4004-400000000000−2222−222200000000000000000000
χ3944-4-400-44000000000002i2−2i2−2i22i200000000000000000000
χ4044-4-400-4400000000000−2i22i22i2−2i200000000000000000000
χ414-44-4-44004i−4i−4i4i0000000000000000000000000000000
χ424-44-4-4400−4i4i4i−4i0000000000000000000000000000000
χ438-8-88000000000000000000000000000000000000000

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