Finite Group Databasebeta

← Group #136288

Character table — Group #136288

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12224444224422448888888822244444444488888888444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ4111111111111111111111111-1-1111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111
χ51111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111
χ61111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ71111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1
χ81111111111111111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-11111
χ91111-1-1-1-111-1-111-1-1iiii−i−i−i−i11-1-11-1-111-1-11ii−i−iii−i−i11-1-1ii−i−ii−ii−ii−i11-1-1
χ101111-1-1-1-111-1-111-1-1iiii−i−i−i−i11-1-11-1-111-1-11ii−i−iii−i−i-1-111−i−iii−ii−iii−i-1-111
χ111111-1-1-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-1111-1-1111−i−iii−i−iii11-1-1−i−iiii−ii−ii−i-1-111
χ121111-1-1-1-111-1-111-1-1iiii−i−i−i−i-1-1-1-1111-1-1111−i−iii−i−iii-1-111ii−i−i−ii−iii−i11-1-1
χ131111-1-1-1-111-1-111-1-1−i−i−i−iiiii11-1-11-1-111-1-11−i−iii−i−iii11-1-1−i−iii−ii−ii−ii11-1-1
χ141111-1-1-1-111-1-111-1-1−i−i−i−iiiii11-1-11-1-111-1-11−i−iii−i−iii-1-111ii−i−ii−ii−i−ii-1-111
χ151111-1-1-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-1111-1-1111ii−i−iii−i−i11-1-1ii−i−i−ii−ii−ii-1-111
χ161111-1-1-1-111-1-111-1-1−i−i−i−iiiii-1-1-1-1111-1-1111ii−i−iii−i−i-1-111−i−iiii−ii−i−ii11-1-1
χ1722222222222222222222222200-2-2-2000000-200000000000000000000-2-20000
χ182222222222222222-2-2-2-2-2-2-2-200-2-2-2000000-200000000000000000000220000
χ19222222222222-2-2-2-20000000000-22-200000022222-2-2-2-2000000000000000000
χ20222222222222-2-2-2-20000000000-22-20000002-2-2-2-22222000000000000000000
χ21222222222222-2-2-2-200000000222-2222-2-2-2-2-200000000000000000000000000
χ22222222222222-2-2-2-200000000-2-22-22-2-22222-200000000000000000000000000
χ232222-2-2-2-222-2-222-2-22i2i2i2i−2i−2i−2i−2i0022-2000000-200000000000000000000−2i2i0000
χ242222-2-2-2-222-2-222-2-2−2i−2i−2i−2i2i2i2i2i0022-2000000-2000000000000000000002i−2i0000
χ252222-2-2-2-222-2-2-2-22200000000002-2-200000022i2i−2i−2i−2i−2i2i2i000000000000000000
χ262222-2-2-2-222-2-2-2-22200000000002-2-20000002−2i−2i2i2i2i2i−2i−2i000000000000000000
χ272222-2-2-2-222-2-2-2-2220000000022-222-2-2-2-222-200000000000000000000000000
χ282222-2-2-2-222-2-2-2-22200000000-2-2-2222222-2-2-200000000000000000000000000
χ2922-2-22i−2i2i−2i2-22i−2i2-22i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000000000001+i−1−i1−i−1+i0000002−2i2−i2
χ3022-2-22i−2i2i−2i2-22i−2i2-22i−2i2ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ3000000000000000000000000−1−i1+i−1+i1−i000000−22−i2i2
χ3122-2-22i−2i2i−2i2-22i−2i2-22i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000000000001+i−1−i1−i−1+i000000−22−i2i2
χ3222-2-22i−2i2i−2i2-22i−2i2-22i−2i−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ3000000000000000000000000−1−i1+i−1+i1−i0000002−2i2−i2
χ3322-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000000000001−i−1+i1+i−1−i000000−22i2−i2
χ3422-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i2ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ000000000000000000000000−1+i1−i−1−i1+i0000002−2−i2i2
χ3522-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000000000001−i−1+i1+i−1−i0000002−2−i2i2
χ3622-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ000000000000000000000000−1+i1−i−1−i1+i000000−22i2−i2
χ3744444444-4-4-4-4000000000000000000000000000000000000000022-2-2000000
χ3844444444-4-4-4-40000000000000000000000000000000000000000-2-222000000
χ394444-4-4-4-4-4-44400000000000000000000000000000000000000002i−2i−2i2i000000
χ404444-4-4-4-4-4-4440000000000000000000000000000000000000000−2i2i2i−2i000000
χ4144-4-44i−4i4i−4i4-44i−4i-44−4i4i0000000000000000000000000000000000000000000000
χ4244-4-44i−4i4i−4i-44−4i4i000000000000000000000000000000002-22i−2i00000000000000
χ4344-4-44i−4i4i−4i-44−4i4i00000000000000000000000000000000-22−2i2i00000000000000
χ4444-4-4−4i4i−4i4i4-4−4i4i-444i−4i0000000000000000000000000000000000000000000000
χ4544-4-4−4i4i−4i4i-444i−4i000000000000000000000000000000002-2−2i2i00000000000000
χ4644-4-4−4i4i−4i4i-444i−4i00000000000000000000000000000000-222i−2i00000000000000
χ474-44-44i−4i−4i4i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ00000002-22i−2i02ζ3−2ζ32ζ−2ζ0000000000000000000000
χ484-44-44i−4i−4i4i000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000000-22−2i2i0−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ494-44-44i−4i−4i4i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ00000002-22i−2i0−2ζ32ζ3−2ζ2ζ0000000000000000000000
χ504-44-44i−4i−4i4i00000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000000-22−2i2i02ζ3−2ζ32ζ−2ζ0000000000000000000000
χ514-44-4−4i4i4i−4i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ300000002-2−2i2i02ζ−2ζ2ζ3−2ζ30000000000000000000000
χ524-44-4−4i4i4i−4i000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000-222i−2i0−2ζ2ζ−2ζ32ζ30000000000000000000000
χ534-44-4−4i4i4i−4i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ300000002-2−2i2i0−2ζ2ζ−2ζ32ζ30000000000000000000000
χ544-44-4−4i4i4i−4i00000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000000-222i−2i02ζ−2ζ2ζ3−2ζ30000000000000000000000
χ554-4-4444-4-4000000002i−2i−2i2i−2i2i2i−2i2-20002-20000000002i−2i2i−2i000000000000000000
χ564-4-4444-4-4000000002i−2i−2i2i−2i2i2i−2i-22000-22000000000−2i2i−2i2i000000000000000000
χ574-4-4444-4-400000000−2i2i2i−2i2i−2i−2i2i2-20002-2000000000−2i2i−2i2i000000000000000000
χ584-4-4444-4-400000000−2i2i2i−2i2i−2i−2i2i-22000-220000000002i−2i2i−2i000000000000000000
χ594-4-44-4-444000000002-2-222-2-222-2000-220000000002-2-22000000000000000000
χ604-4-44-4-444000000002-2-222-2-22-220002-2000000000-222-2000000000000000000
χ614-4-44-4-44400000000-222-2-222-22-2000-22000000000-222-2000000000000000000
χ624-4-44-4-44400000000-222-2-222-2-220002-20000000002-2-22000000000000000000

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