Finite Group Databasebeta

← Group #9239

Character table — Group #9239

Order 256.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43
size11112222222244444444444888888888888888816161616
order1222224444442222444888824444488888888884488
χ11111111111111111111111111111111111111111111
χ21111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111
χ41111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111-1-1
χ51111111111111-1-111-1-11111-1-11111111111-1-1-1-1-1-1-1-1
χ61111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ71111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-1
χ81111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111
χ911111111-1-1-1-1-111-11-1-1ii−i−i1-1ii−i−i11-1-1i−iii−i−i1-1i−i
χ1011111111-1-1-1-1-111-11-1-1ii−i−i1-1−i−iii-1-111i−iii−i−i-11−ii
χ1111111111-1-1-1-1-111-11-1-1−i−iii1-1ii−i−i-1-111−ii−i−iii-11i−i
χ1211111111-1-1-1-1-111-11-1-1−i−iii1-1−i−iii11-1-1−ii−i−iii1-1−ii
χ1311111111-1-1-1-1-1-1-1-1111ii−i−i-11ii−i−i11-1-1i−i−i−iii-11−ii
χ1411111111-1-1-1-1-1-1-1-1111ii−i−i-11−i−iii-1-111i−i−i−iii1-1i−i
χ1511111111-1-1-1-1-1-1-1-1111−i−iii-11ii−i−i-1-111−iiii−i−i1-1−ii
χ1611111111-1-1-1-1-1-1-1-1111−i−iii-11−i−iii11-1-1−iiii−i−i-11i−i
χ17222222-2-22222-200-2-20022220000000000-2-200000000
χ18222222-2-22222-200-2-200-2-2-2-200000000002200000000
χ19222222-2-2-2-2-2-22002-2002i2i−2i−2i0000000000−2i2i00000000
χ20222222-2-2-2-2-2-22002-200−2i−2i2i2i00000000002i−2i00000000
χ212222-2-22222-2-2-2222-2-2-20000-22000000000000000000
χ222222-2-22222-2-2-2-2-22-22200002-2000000000000000000
χ232222-2-222-2-222222-2-2220000-2-2000000000000000000
χ242222-2-222-2-2222-2-2-2-2-2-2000022000000000000000000
χ252222-2-2-2-222-2-2200-220000000000000000002i−2i2i−2i0000
χ262222-2-2-2-222-2-2200-22000000000000000000−2i2i−2i2i0000
χ272222-2-2-2-2-2-222-200220000000000000000002-2-220000
χ282222-2-2-2-2-2-222-20022000000000000000000-222-20000
χ292-22-22-2002i−2i2i−2i00000002ζ−2ζ2ζ3−2ζ3001+i−1−i1−i−1+i2−2i2−i20000000000
χ302-22-22-2002i−2i2i−2i00000002ζ−2ζ2ζ3−2ζ300−1−i1+i−1+i1−i−22−i2i20000000000
χ312-22-22-2002i−2i2i−2i0000000−2ζ2ζ−2ζ32ζ3001+i−1−i1−i−1+i−22−i2i20000000000
χ322-22-22-2002i−2i2i−2i0000000−2ζ2ζ−2ζ32ζ300−1−i1+i−1+i1−i2−2i2−i20000000000
χ332-22-22-200−2i2i−2i2i00000002ζ3−2ζ32ζ−2ζ001−i−1+i1+i−1−i−22i2−i20000000000
χ342-22-22-200−2i2i−2i2i00000002ζ3−2ζ32ζ−2ζ00−1+i1−i−1−i1+i2−2−i2i20000000000
χ352-22-22-200−2i2i−2i2i0000000−2ζ32ζ3−2ζ2ζ001−i−1+i1+i−1−i2−2−i2i20000000000
χ362-22-22-200−2i2i−2i2i0000000−2ζ32ζ3−2ζ2ζ00−1+i1−i−1−i1+i−22i2−i20000000000
χ374-44-4-44004i−4i−4i4i0000000000000000000000000000000
χ384-44-4-4400−4i4i4i−4i0000000000000000000000000000000
χ394-4-44004-40000000004-4000000000000000000000000
χ404-4-44004-4000000000-44000000000000000000000000
χ414-4-4400-44000004-40000000000000000000000000000
χ424-4-4400-4400000-440000000000000000000000000000
χ4388-8-8000000000000000000000000000000000000000

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