Finite Group Databasebeta

← Group #137313

Character table — Group #137313

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12224444224422442244444488888888888844444488888888888888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ51111111111111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1
χ91111-1-1-1-111-1-111-1-111-1-11-11-1ii−i−iii−i−iii−i−i11-1-11-1i−iii−i−i11-1-1ii−i−i
χ101111-1-1-1-111-1-111-1-111-1-11-11-1ii−i−iii−i−iii−i−i-1-1111-1i−i−i−iii-1-111−i−iii
χ111111-1-1-1-111-1-111-1-111-1-11-11-1−i−iii−i−iii−i−iii11-1-11-1−ii−i−iii11-1-1−i−iii
χ121111-1-1-1-111-1-111-1-111-1-11-11-1−i−iii−i−iii−i−iii-1-1111-1−iiii−i−i-1-111ii−i−i
χ131111-1-1-1-111-1-111-1-1-1-1111-11-1ii−i−iii−i−i−i−iii11-1-1-11−iiii−i−i-1-111−i−iii
χ141111-1-1-1-111-1-111-1-1-1-1111-11-1ii−i−iii−i−i−i−iii-1-111-11−ii−i−iii11-1-1ii−i−i
χ151111-1-1-1-111-1-111-1-1-1-1111-11-1−i−iii−i−iiiii−i−i11-1-1-11i−i−i−iii-1-111ii−i−i
χ161111-1-1-1-111-1-111-1-1-1-1111-11-1−i−iii−i−iiiii−i−i-1-111-11i−iii−i−i11-1-1−i−iii
χ1722222222222222220000-2-2-2-22222-2-2-2-2000000000000000000000000
χ1822222222222222220000-2-2-2-2-2-2-2-22222000000000000000000000000
χ19222222222222-2-2-2-200002-2-22000000002222000000-2-2000000000000
χ20222222222222-2-2-2-200002-2-2200000000-2-2-2-200000022000000000000
χ21222222222222-2-2-2-22222-222-20000000000000000-2-200000000000000
χ22222222222222-2-2-2-2-2-2-2-2-222-200000000000000002200000000000000
χ232222-2-2-2-222-2-222-2-20000-22-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ242222-2-2-2-222-2-222-2-20000-22-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ252222-2-2-2-222-2-2-2-222000022-2-2000000002i2i−2i−2i000000−2i2i000000000000
χ262222-2-2-2-222-2-2-2-222000022-2-200000000−2i−2i2i2i0000002i−2i000000000000
χ272222-2-2-2-222-2-2-2-22222-2-2-2-2220000000000000000-2200000000000000
χ282222-2-2-2-222-2-2-2-222-2-222-2-22200000000000000002-200000000000000
χ2922-2-222-2-2-222-22-2-220000000000002i−2i2i−2i0000000000000000i2−i2i2−i22−22−2
χ3022-2-222-2-2-222-22-2-220000000000002i−2i2i−2i0000000000000000−i2i2−i2i2−22−22
χ3122-2-222-2-2-222-22-2-22000000000000−2i2i−2i2i0000000000000000i2−i2i2−i2−22−22
χ3222-2-222-2-2-222-22-2-22000000000000−2i2i−2i2i0000000000000000−i2i2−i2i22−22−2
χ3322-2-2-2-222-22-222-22-20000000000002-2-220000000000000000i2−i2−i2i2−i2i2i2−i2
χ3422-2-2-2-222-22-222-22-20000000000002-2-220000000000000000−i2i2i2−i2i2−i2−i2i2
χ3522-2-2-2-222-22-222-22-2000000000000-222-20000000000000000i2−i2−i2i2i2−i2−i2i2
χ3622-2-2-2-222-22-222-22-2000000000000-222-20000000000000000−i2i2i2−i2−i2i2i2−i2
χ3744444444-4-4-4-40000000000000000000000002-22-20000000000000000
χ3844444444-4-4-4-4000000000000000000000000-22-220000000000000000
χ394444-4-4-4-4-4-4440000000000000000000000002-2-220000000000000000
χ404444-4-4-4-4-4-444000000000000000000000000-222-20000000000000000
χ4144-4-444-4-44-4-44000000000000000000000000000000002i−2i2i−2i00000000
χ4244-4-444-4-44-4-4400000000000000000000000000000000−2i2i−2i2i00000000
χ4344-4-444-4-4-444-4-444-40000000000000000000000000000000000000000
χ4444-4-4-4-4444-44-4000000000000000000000000000000002-2-2200000000
χ4544-4-4-4-4444-44-400000000000000000000000000000000-222-200000000
χ4644-4-4-4-444-44-44-44-440000000000000000000000000000000000000000
χ474-44-44i−4i4i−4i000000002-22i−2i00002ζ−2ζ2ζ3−2ζ300002ζ−2ζ2ζ3−2ζ300000000000000000000
χ484-44-44i−4i4i−4i000000002-22i−2i0000−2ζ2ζ−2ζ32ζ30000−2ζ2ζ−2ζ32ζ300000000000000000000
χ494-44-44i−4i4i−4i00000000-22−2i2i00002ζ−2ζ2ζ3−2ζ30000−2ζ2ζ−2ζ32ζ300000000000000000000
χ504-44-44i−4i4i−4i00000000-22−2i2i0000−2ζ2ζ−2ζ32ζ300002ζ−2ζ2ζ3−2ζ300000000000000000000
χ514-44-4−4i4i−4i4i000000002-2−2i2i00002ζ3−2ζ32ζ−2ζ00002ζ3−2ζ32ζ−2ζ00000000000000000000
χ524-44-4−4i4i−4i4i000000002-2−2i2i0000−2ζ32ζ3−2ζ2ζ0000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ534-44-4−4i4i−4i4i00000000-222i−2i00002ζ3−2ζ32ζ−2ζ0000−2ζ32ζ3−2ζ2ζ00000000000000000000
χ544-44-4−4i4i−4i4i00000000-222i−2i0000−2ζ32ζ3−2ζ2ζ00002ζ3−2ζ32ζ−2ζ00000000000000000000
χ558-8-888i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000

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