Finite Group Databasebeta

← Group #125478

Character table — Group #125478

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12222222222244444444444444444444224444448888888888888888
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
χ51111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ61111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ71111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111−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
χ13111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111ii−i−i−i−iiiii−i−i−i−iii
χ14111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i
χ15111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ17222222222222222222-2-222-2-222-2-2-2-2-2-2000000000000000000000000
χ182222222222222222-2-222-2-222-2-2-2-2-2-222000000000000000000000000
χ19222222222222-2-2-2-222-2-222-2-2-2-222-2-222000000000000000000000000
χ20222222222222-2-2-2-2-2-222-2-2222222-2-2-2-2000000000000000000000000
χ2122-22-2-2-2222-2-200002i−2i2i−2i2i−2i2i−2i00002-2000000000000000000002ζ−2ζ002ζ3−2ζ3
χ2222-22-2-2-2222-2-200002i−2i2i−2i2i−2i2i−2i00002-200000000000000000000−2ζ2ζ00−2ζ32ζ3
χ2322-22-2-2-2222-2-200002i−2i−2i2i2i−2i−2i2i0000-220000000000000000002ζ−2ζ002ζ3−2ζ300
χ2422-22-2-2-2222-2-200002i−2i−2i2i2i−2i−2i2i0000-22000000000000000000−2ζ2ζ00−2ζ32ζ300
χ2522-22-2-2-2222-2-20000−2i2i2i−2i−2i2i2i−2i0000-220000000000000000002ζ3−2ζ3002ζ−2ζ00
χ2622-22-2-2-2222-2-20000−2i2i2i−2i−2i2i2i−2i0000-22000000000000000000−2ζ32ζ300−2ζ2ζ00
χ2722-22-2-2-2222-2-20000−2i2i−2i2i−2i2i−2i2i00002-2000000000000000000002ζ3−2ζ3002ζ−2ζ
χ2822-22-2-2-2222-2-20000−2i2i−2i2i−2i2i−2i2i00002-200000000000000000000−2ζ32ζ300−2ζ2ζ
χ292-2-2222-2-22-22-20000002i−2i00−2i2i2-22i−2i0000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00000000
χ302-2-2222-2-22-22-20000002i−2i00−2i2i2-22i−2i000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00000000
χ312-2-2222-2-22-22-20000002i−2i00−2i2i-22−2i2i0000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00000000
χ322-2-2222-2-22-22-20000002i−2i00−2i2i-22−2i2i000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00000000
χ332-2-2222-2-22-22-2000000−2i2i002i−2i2-2−2i2i0000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00000000
χ342-2-2222-2-22-22-2000000−2i2i002i−2i2-2−2i2i000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00000000
χ352-2-2222-2-22-22-2000000−2i2i002i−2i-222i−2i0000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00000000
χ362-2-2222-2-22-22-2000000−2i2i002i−2i-222i−2i000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00000000
χ3744444444-4-4-4-444-4-40000000000000000000000000000000000000000
χ3844444444-4-4-4-4-4-4440000000000000000000000000000000000000000
χ3944-44-4-4-44-4-4440000000000000000004-4000000000000000000000000
χ4044-44-4-4-44-4-444000000000000000000-44000000000000000000000000
χ4144-4-44-44-40000004i−4i000000000000000000002-22i−2i0000000000000000
χ4244-4-44-44-40000004i−4i00000000000000000000-22−2i2i0000000000000000
χ4344-4-44-44-4000000−4i4i000000000000000000002-2−2i2i0000000000000000
χ4444-4-44-44-4000000−4i4i00000000000000000000-222i−2i0000000000000000
χ454-444-4-44-44-4-440000004400-4-400000000000000000000000000000000
χ464-444-4-44-44-4-44000000-4-4004400000000000000000000000000000000
χ474-444-4-44-4-444-400004i−4i00−4i4i0000000000000000000000000000000000
χ484-444-4-44-4-444-40000−4i4i004i−4i0000000000000000000000000000000000
χ494-4-4444-4-4-44-4400004400-4-40000000000000000000000000000000000
χ504-4-4444-4-4-44-440000-4-400440000000000000000000000000000000000
χ514-4-4-4-444400004-40000000000000000002-22-200000000000000000000
χ524-4-4-4-444400004-4000000000000000000-22-2200000000000000000000
χ534-4-4-4-44440000-440000000000000000002-2-2200000000000000000000
χ544-4-4-4-44440000-44000000000000000000-222-200000000000000000000
χ55888-8-88-8-8000000000000000000000000000000000000000000000000
χ568-88-88-8-88000000000000000000000000000000000000000000000000

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