Finite Group Databasebeta

← Group #137421

Character table — Group #137421

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12224444224422448888888844444444444488888888224444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ51111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-11111-1-1-1-1
χ91111-1-1-1-111-1-1-1-111iiii−i−i−i−i1-111-1-111-1-11-1ii−i−iii−i−i1-11-1ii−i−ii−i11-1-1ii−i−i
χ101111-1-1-1-111-1-1-1-111iiii−i−i−i−i1-111-1-111-1-11-1ii−i−iii−i−i-11-11−i−iiii−i-1-111−i−iii
χ111111-1-1-1-111-1-1-1-111iiii−i−i−i−i1-1-1-111-1-1111-1−i−iii−i−iii1-11-1ii−i−ii−i-1-111−i−iii
χ121111-1-1-1-111-1-1-1-111iiii−i−i−i−i1-1-1-111-1-1111-1−i−iii−i−iii-11-11−i−iiii−i11-1-1ii−i−i
χ131111-1-1-1-111-1-1-1-111−i−i−i−iiiii1-111-1-111-1-11-1−i−iii−i−iii1-11-1−i−iii−ii11-1-1−i−iii
χ141111-1-1-1-111-1-1-1-111−i−i−i−iiiii1-111-1-111-1-11-1−i−iii−i−iii-11-11ii−i−i−ii-1-111ii−i−i
χ151111-1-1-1-111-1-1-1-111−i−i−i−iiiii1-1-1-111-1-1111-1ii−i−iii−i−i1-11-1−i−iii−ii-1-111ii−i−i
χ161111-1-1-1-111-1-1-1-111−i−i−i−iiiii1-1-1-111-1-1111-1ii−i−iii−i−i-11-11ii−i−i−ii11-1-1−i−iii
χ17222222222222222222222222-2-200000000-2-20000000000000000-2-200000000
χ182222222222222222-2-2-2-2-2-2-2-2-2-200000000-2-200000000000000002200000000
χ19222222222222-2-2-2-2000000002-200000000-222222-2-2-2-2000000000000000000
χ20222222222222-2-2-2-2000000002-200000000-22-2-2-2-22222000000000000000000
χ21222222222222-2-2-2-200000000-222222-2-2-2-22-200000000000000000000000000
χ22222222222222-2-2-2-200000000-22-2-2-2-222222-200000000000000000000000000
χ232222-2-2-2-222-2-222-2-2000000002200000000-2-22i2i−2i−2i−2i−2i2i2i000000000000000000
χ242222-2-2-2-222-2-222-2-2000000002200000000-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000
χ252222-2-2-2-222-2-222-2-200000000-2-222-2-2-2-2222200000000000000000000000000
χ262222-2-2-2-222-2-222-2-200000000-2-2-2-22222-2-22200000000000000000000000000
χ272222-2-2-2-222-2-2-2-2222i2i2i2i−2i−2i−2i−2i-2200000000-220000000000000000−2i2i00000000
χ282222-2-2-2-222-2-2-2-222−2i−2i−2i−2i2i2i2i2i-2200000000-2200000000000000002i−2i00000000
χ292-2-2222-2-22-22-2-222-222-2-222-2-2000000000000000000000000000000i2−i2i2−i2i2−i2i2−i2
χ302-2-2222-2-22-22-2-222-222-2-222-2-2000000000000000000000000000000−i2i2−i2i2−i2i2−i2i2
χ312-2-2222-2-22-22-2-222-2-2-222-2-222000000000000000000000000000000i2−i2i2−i2−i2i2−i2i2
χ322-2-2222-2-22-22-2-222-2-2-222-2-222000000000000000000000000000000−i2i2−i2i2i2−i2i2−i2
χ332-2-22-2-2222-2-222-22-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000i2−i2−i2i2−222−2
χ342-2-22-2-2222-2-222-22-22i2i−2i−2i−2i−2i2i2i000000000000000000000000000000−i2i2i2−i22−2−22
χ352-2-22-2-2222-2-222-22-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000i2−i2−i2i22−2−22
χ362-2-22-2-2222-2-222-22-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000−i2i2i2−i2−222−2
χ3744444444-4-4-4-4000000000000000000000000000000002-2-2200000000000000
χ3844444444-4-4-4-400000000000000000000000000000000-222-200000000000000
χ394444-4-4-4-4-4-4440000000000000000000000000000000022-2-200000000000000
χ404444-4-4-4-4-4-44400000000000000000000000000000000-2-22200000000000000
χ4144-4-44i−4i4i−4i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3002-22i−2i0000002ζ−2ζ2ζ3−2ζ30000000000000000000000
χ4244-4-44i−4i4i−4i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300-22−2i2i000000−2ζ2ζ−2ζ32ζ30000000000000000000000
χ4344-4-44i−4i4i−4i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3002-22i−2i000000−2ζ2ζ−2ζ32ζ30000000000000000000000
χ4444-4-44i−4i4i−4i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300-22−2i2i0000002ζ−2ζ2ζ3−2ζ30000000000000000000000
χ4544-4-4−4i4i−4i4i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ002-2−2i2i0000002ζ3−2ζ32ζ−2ζ0000000000000000000000
χ4644-4-4−4i4i−4i4i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00-222i−2i000000−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ4744-4-4−4i4i−4i4i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ002-2−2i2i000000−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ4844-4-4−4i4i−4i4i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00-222i−2i0000002ζ3−2ζ32ζ−2ζ0000000000000000000000
χ494-44-44i−4i−4i4i000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000002-22i−2i0000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ504-44-44i−4i−4i4i000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3000000-22−2i2i000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ514-44-44i−4i−4i4i00000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000002-22i−2i000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ524-44-44i−4i−4i4i00000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3000000-22−2i2i0000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ534-44-4−4i4i4i−4i000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000002-2−2i2i0000002ζ3−2ζ32ζ−2ζ000000000000000000
χ544-44-4−4i4i4i−4i000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ000000-222i−2i000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ554-44-4−4i4i4i−4i00000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000002-2−2i2i000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ564-44-4−4i4i4i−4i00000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ000000-222i−2i0000002ζ3−2ζ32ζ−2ζ000000000000000000
χ574-4-4444-4-44-44-44-4-440000000000000000000000000000000000000000000000
χ584-4-4444-4-4-44-440000000000000000000000000000000000002i−2i2i−2i0000000000
χ594-4-4444-4-4-44-44000000000000000000000000000000000000−2i2i−2i2i0000000000
χ604-4-44-4-4444-4-44-44-440000000000000000000000000000000000000000000000
χ614-4-44-4-444-444-40000000000000000000000000000000000002-2-220000000000
χ624-4-44-4-444-444-4000000000000000000000000000000000000-222-20000000000

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