Finite Group Databasebeta

← Group #101356

Character table — Group #101356

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222222224444448888888888161616161616161616161616161616161616161616161616
order12222222444444442244444488888888444444444444888888888888
χ111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-111-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-1111-1-11-1-11111-1-1-1-11111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ911111111-1-1-1-1-1-1-1-1-1-111111-1iiii−i−i−i−i11-111-1-1-1ii−i−iii−i−iii−i−i11-1-1
χ1011111111-1-1-1-1-1-1-1-1-1-111111-1iiii−i−i−i−i11-1-1-1-111−i−iiiii−i−i−i−iii-1-111
χ1111111111-1-1-1-1-1-1-1-1-1-111111-1iiii−i−i−i−i-1-11111-1-1−i−iii−i−iiiii−i−i-1-111
χ1211111111-1-1-1-1-1-1-1-1-1-111111-1iiii−i−i−i−i-1-11-1-1111ii−i−i−i−iii−i−iii11-1-1
χ1311111111-1-1-1-1-1-1-1-1-1-111111-1−i−i−i−iiiii11-111-1-1-1−i−iii−i−iii−i−iii11-1-1
χ1411111111-1-1-1-1-1-1-1-1-1-111111-1−i−i−i−iiiii11-1-1-1-111ii−i−i−i−iiiii−i−i-1-111
χ1511111111-1-1-1-1-1-1-1-1-1-111111-1−i−i−i−iiiii-1-11111-1-1ii−i−iii−i−i−i−iii-1-111
χ1611111111-1-1-1-1-1-1-1-1-1-111111-1−i−i−i−iiiii-1-11-1-1111−i−iiiii−i−iii−i−i11-1-1
χ172222222222222222-2-222-2-2-2-222-2-222-2-2000000000000000000000000
χ182222222222222222-2-222-2-2-2-2-2-222-2-222000000000000000000000000
χ192222222222-2-2-2-22222-2-222-2-2000000002-2200-2000000000000000000
χ202222222222-2-2-2-22222-2-222-2-200000000-22-2002000000000000000000
χ212222222222-2-2-2-222-2-2-2-2-2-222000000000000000000002i−2i2i−2i00000000
χ222222222222-2-2-2-222-2-2-2-2-2-22200000000000000000000−2i2i−2i2i00000000
χ2322222222-2-22222-2-222-2-2-2-22-2000000000000000000002-2-2200000000
χ2422222222-2-22222-2-222-2-2-2-22-200000000000000000000-222-200000000
χ2522222222-2-22222-2-2-2-2-2-222-22000000002-2-2002000000000000000000
χ2622222222-2-22222-2-2-2-2-2-222-2200000000-22200-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ292-22-222-2-22i−2i2i2i−2i−2i2i−2i002-20000002ζ3−2ζ3002ζ−2ζ000000001−i−1+i1+i−1−i000000002−2i2−i2
χ302-22-222-2-22i−2i2i2i−2i−2i2i−2i002-20000002ζ3−2ζ3002ζ−2ζ00000000−1+i1−i−1−i1+i00000000−22−i2i2
χ312-22-222-2-22i−2i2i2i−2i−2i2i−2i002-2000000−2ζ32ζ300−2ζ2ζ000000001−i−1+i1+i−1−i00000000−22−i2i2
χ322-22-222-2-22i−2i2i2i−2i−2i2i−2i002-2000000−2ζ32ζ300−2ζ2ζ00000000−1+i1−i−1−i1+i000000002−2i2−i2
χ332-22-222-2-2−2i2i−2i−2i2i2i−2i2i002-20000002ζ−2ζ002ζ3−2ζ3000000001+i−1−i1−i−1+i00000000−22i2−i2
χ342-22-222-2-2−2i2i−2i−2i2i2i−2i2i002-20000002ζ−2ζ002ζ3−2ζ300000000−1−i1+i−1+i1−i000000002−2−i2i2
χ352-22-222-2-2−2i2i−2i−2i2i2i−2i2i002-2000000−2ζ2ζ00−2ζ32ζ3000000001+i−1−i1−i−1+i000000002−2−i2i2
χ362-22-222-2-2−2i2i−2i−2i2i2i−2i2i002-2000000−2ζ2ζ00−2ζ32ζ300000000−1−i1+i−1+i1−i00000000−22i2−i2
χ37444-4-4-44-4440000-4-44-400-440000000000000000000000000000000000
χ38444-4-4-44-4440000-4-4-44004-40000000000000000000000000000000000
χ39444-4-4-44-4-4-40000444-4004-40000000000000000000000000000000000
χ40444-4-4-44-4-4-4000044-4400-440000000000000000000000000000000000
χ4144-4-44-4-44004i−4i4i−4i00000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ4244-4-44-4-44004i−4i4i−4i0000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ4344-4-44-4-4400−4i4i−4i4i00000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ4444-4-44-4-4400−4i4i−4i4i0000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ454-444-4-4-444i−4i0000−4i4i000000002−2i−2+2i002+2i−2−2i00000000000000000000000000
χ464-444-4-4-444i−4i0000−4i4i00000000−2+2i2−2i00−2−2i2+2i00000000000000000000000000
χ474-444-4-4-44−4i4i00004i−4i000000002+2i−2−2i002−2i−2+2i00000000000000000000000000
χ484-444-4-4-44−4i4i00004i−4i00000000−2−2i2+2i00−2+2i2−2i00000000000000000000000000
χ494-44-444-4-44i−4i−4i−4i4i4i4i−4i00-44000000000000000000000000000000000000
χ504-44-444-4-4−4i4i4i4i−4i−4i−4i4i00-44000000000000000000000000000000000000
χ514-4-444-44-4004-4-440000000000000000000002i−2i02i−2i0000000000000000
χ524-4-444-44-4004-4-44000000000000000000000−2i2i0−2i2i0000000000000000
χ534-4-444-44-400-444-40000000000000000000002i−2i0−2i2i0000000000000000
χ544-4-444-44-400-444-4000000000000000000000−2i2i02i−2i0000000000000000
χ5588-88-88-8-8000000000000000000000000000000000000000000000000
χ568-8-8-8-8888000000000000000000000000000000000000000000000000

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