Finite Group Databasebeta

← Group #136304

Character table — Group #136304

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12224444224422442444444488888888888844444444448888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1
χ51111111111111111111-1-1-1-111111-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-1
χ61111111111111111111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ71111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1
χ81111111111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ91111-1-1-1-111-1-111-1-1-11-111-1-11ii−i−iii−i−iii−i−i1-111-1-1ii−i−ii−ii−ii−i11-1-1
χ101111-1-1-1-111-1-111-1-1-11-111-1-11ii−i−iii−i−iii−i−i1-1-1-111−i−iii−ii−iii−i-1-111
χ111111-1-1-1-111-1-111-1-1-11-111-1-11−i−iii−i−iii−i−iii1-111-1-1−i−iii−ii−ii−ii11-1-1
χ121111-1-1-1-111-1-111-1-1-11-111-1-11−i−iii−i−iii−i−iii1-1-1-111ii−i−ii−ii−i−ii-1-111
χ131111-1-1-1-111-1-111-1-1-11-1-1-1111ii−i−i−i−iiiii−i−i-1111-1-1−i−iiii−ii−i−ii-1-111
χ141111-1-1-1-111-1-111-1-1-11-1-1-1111ii−i−i−i−iiiii−i−i-11-1-111ii−i−i−ii−ii−ii11-1-1
χ151111-1-1-1-111-1-111-1-1-11-1-1-1111−i−iiiii−i−i−i−iii-1111-1-1ii−i−i−ii−iii−i-1-111
χ161111-1-1-1-111-1-111-1-1-11-1-1-1111−i−iiiii−i−i−i−iii-11-1-111−i−iiii−ii−ii−i11-1-1
χ172222222222222222-2-2-20000-222220000-2-2-2-200000000000000000000
χ182222222222222222-2-2-20000-2-2-2-2-20000222200000000000000000000
χ19222222222222-2-2-2-222-22222-2000000000000-2-2000000000000000000
χ20222222222222-2-2-2-222-2-2-2-2-2-200000000000022000000000000000000
χ21222222222222-2-2-2-2-2-220000200002222000000000000000000-2-20000
χ22222222222222-2-2-2-2-2-22000020000-2-2-2-2000000000000000000220000
χ232222-2-2-2-222-2-222-2-22-220000-22i2i−2i−2i0000−2i−2i2i2i00000000000000000000
χ242222-2-2-2-222-2-222-2-22-220000-2−2i−2i2i2i00002i2i−2i−2i00000000000000000000
χ252222-2-2-2-222-2-2-2-2222-2-20000200002i2i−2i−2i000000000000000000−2i2i0000
χ262222-2-2-2-222-2-2-2-2222-2-2000020000−2i−2i2i2i0000000000000000002i−2i0000
χ272222-2-2-2-222-2-2-2-222-22222-2-2-2000000000000-22000000000000000000
χ282222-2-2-2-222-2-2-2-222-222-2-222-20000000000002-2000000000000000000
χ2922-2-22i−2i2i−2i2-22i−2i2-22i−2i00000000000000002ζ3−2ζ32ζ−2ζ0000001−i−1+i1+i−1−i0000002−2i2−i2
χ3022-2-22i−2i2i−2i2-22i−2i2-22i−2i00000000000000002ζ3−2ζ32ζ−2ζ000000−1+i1−i−1−i1+i000000−22−i2i2
χ3122-2-22i−2i2i−2i2-22i−2i2-22i−2i0000000000000000−2ζ32ζ3−2ζ2ζ0000001−i−1+i1+i−1−i000000−22−i2i2
χ3222-2-22i−2i2i−2i2-22i−2i2-22i−2i0000000000000000−2ζ32ζ3−2ζ2ζ000000−1+i1−i−1−i1+i0000002−2i2−i2
χ3322-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i00000000000000002ζ−2ζ2ζ3−2ζ30000001+i−1−i1−i−1+i000000−22i2−i2
χ3422-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i00000000000000002ζ−2ζ2ζ3−2ζ3000000−1−i1+i−1+i1−i0000002−2−i2i2
χ3522-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i0000000000000000−2ζ2ζ−2ζ32ζ30000001+i−1−i1−i−1+i0000002−2−i2i2
χ3622-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i0000000000000000−2ζ2ζ−2ζ32ζ3000000−1−i1+i−1+i1−i000000−22i2−i2
χ3744444444-4-4-4-4000000000000000000000000000000000022-2-2000000
χ3844444444-4-4-4-40000000000000000000000000000000000-2-222000000
χ394444-4-4-4-4-4-44400000000000000000000000000000000002i−2i−2i2i000000
χ404444-4-4-4-4-4-4440000000000000000000000000000000000−2i2i2i−2i000000
χ4144-4-44i−4i4i−4i4-44i−4i-44−4i4i0000000000000000000000000000000000000000
χ4244-4-44i−4i4i−4i-44−4i4i000000000000000000000000002i−2i2-200000000000000
χ4344-4-44i−4i4i−4i-44−4i4i00000000000000000000000000−2i2i-2200000000000000
χ4444-4-4−4i4i−4i4i4-4−4i4i-444i−4i0000000000000000000000000000000000000000
χ4544-4-4−4i4i−4i4i-444i−4i000000000000000000000000002i−2i-2200000000000000
χ4644-4-4−4i4i−4i4i-444i−4i00000000000000000000000000−2i2i2-200000000000000
χ474-44-44i−4i−4i4i000000000002i−2i2-202ζ3−2ζ32ζ−2ζ2ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ484-44-44i−4i−4i4i000000000002i−2i2-20−2ζ32ζ3−2ζ2ζ−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ494-44-44i−4i−4i4i00000000000−2i2i-2202ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ32ζ3000000000000000000000000
χ504-44-44i−4i−4i4i00000000000−2i2i-220−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ3−2ζ3000000000000000000000000
χ514-44-4−4i4i4i−4i000000000002i−2i-2202ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ524-44-4−4i4i4i−4i000000000002i−2i-220−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ−2ζ000000000000000000000000
χ534-44-4−4i4i4i−4i00000000000−2i2i2-202ζ−2ζ2ζ3−2ζ32ζ3−2ζ32ζ−2ζ000000000000000000000000
χ544-44-4−4i4i4i−4i00000000000−2i2i2-20−2ζ2ζ−2ζ32ζ3−2ζ32ζ3−2ζ2ζ000000000000000000000000
χ558-8-8888-8-8000000000000000000000000000000000000000000000000
χ568-8-88-8-888000000000000000000000000000000000000000000000000

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