Finite Group Databasebeta

← Group #125613

Character table — Group #125613

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222244444444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111111111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-111-1-1
χ10111111111111-1-1-1-111111111-1-1-1-111-1-111-1-111-1-1-1-111-1-111-1-111-1-111
χ11111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ12111111111111-1-1-1-111111111-1-1-1-111-1-1-1-111-1-111-1-111-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-2-2-222-2-2-2-2-2-222000000000000000000000000
χ182222222222222222-2-22222-2-2-2-222-2-2-2-2000000000000000000000000
χ19222222222222-2-2-2-222-2-2-2-2222222-2-2-2-2000000000000000000000000
χ20222222222222-2-2-2-2-2-22222-2-222-2-2-2-222000000000000000000000000
χ2122-2-2-2-22222-2-200002i−2i2i2i−2i−2i2i−2i00002-20000000000002ζ3−2ζ3002ζ−2ζ00000000
χ2222-2-2-2-22222-2-200002i−2i2i2i−2i−2i2i−2i00002-2000000000000−2ζ32ζ300−2ζ2ζ00000000
χ2322-2-2-2-22222-2-200002i−2i−2i−2i2i2i2i−2i0000-2200000000002ζ3−2ζ3002ζ−2ζ0000000000
χ2422-2-2-2-22222-2-200002i−2i−2i−2i2i2i2i−2i0000-220000000000−2ζ32ζ300−2ζ2ζ0000000000
χ2522-2-2-2-22222-2-20000−2i2i2i2i−2i−2i−2i2i0000-2200000000002ζ−2ζ002ζ3−2ζ30000000000
χ2622-2-2-2-22222-2-20000−2i2i2i2i−2i−2i−2i2i0000-220000000000−2ζ2ζ00−2ζ32ζ30000000000
χ2722-2-2-2-22222-2-20000−2i2i−2i−2i2i2i−2i2i00002-20000000000002ζ−2ζ002ζ3−2ζ300000000
χ2822-2-2-2-22222-2-20000−2i2i−2i−2i2i2i−2i2i00002-2000000000000−2ζ2ζ00−2ζ32ζ300000000
χ292-2-222-22-22-22-20000002-22-2002i−2i00002i−2i00000000000000002−2i2−i22−2i2−i2
χ302-2-222-22-22-22-20000002-22-2002i−2i00002i−2i0000000000000000−22−i2i2−22−i2i2
χ312-2-222-22-22-22-20000002-22-200−2i2i0000−2i2i00000000000000002−2−i2i22−2−i2i2
χ322-2-222-22-22-22-20000002-22-200−2i2i0000−2i2i0000000000000000−22i2−i2−22i2−i2
χ332-2-222-22-22-22-2000000-22-22002i−2i0000−2i2i0000000000000000i2−i2−22−i2i22−2
χ342-2-222-22-22-22-2000000-22-22002i−2i0000−2i2i0000000000000000−i2i22−2i2−i2−22
χ352-2-222-22-22-22-2000000-22-2200−2i2i00002i−2i0000000000000000i2−i22−2−i2i2−22
χ362-2-222-22-22-22-2000000-22-2200−2i2i00002i−2i0000000000000000−i2i2−22i2−i22−2
χ3744444444-4-4-4-444-4-40000000000000000000000000000000000000000
χ3844444444-4-4-4-4-4-4440000000000000000000000000000000000000000
χ394444-4-4-4-40000004-4000000000000000000002-22-20000000000000000
χ404444-4-4-4-40000004-400000000000000000000-22-220000000000000000
χ414444-4-4-4-4000000-44000000000000000000002-2-220000000000000000
χ424444-4-4-4-4000000-4400000000000000000000-222-20000000000000000
χ4344-4-4-4-444-4-444000000000000004-40000000000000000000000000000
χ4444-4-4-4-444-4-44400000000000000-440000000000000000000000000000
χ454-44-44-4-4400004i−4i0000000000000000002i−2i2-200000000000000000000
χ464-44-44-4-4400004i−4i000000000000000000−2i2i-2200000000000000000000
χ474-44-44-4-440000−4i4i0000000000000000002i−2i-2200000000000000000000
χ484-44-44-4-440000−4i4i000000000000000000−2i2i2-200000000000000000000
χ494-44-4-444-44-4-440000004i−4i−4i4i0000000000000000000000000000000000
χ504-44-4-444-44-4-44000000−4i4i4i−4i0000000000000000000000000000000000
χ514-44-4-444-4-444-40000440000-4-400000000000000000000000000000000
χ524-44-4-444-4-444-40000-4-400004400000000000000000000000000000000
χ534-4-444-44-4-44-4400004i−4i0000−4i4i00000000000000000000000000000000
χ544-4-444-44-4-44-440000−4i4i00004i−4i00000000000000000000000000000000
χ5588-8-888-8-8000000000000000000000000000000000000000000000000
χ568-8-88-88-88000000000000000000000000000000000000000000000000

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