Finite Group Databasebeta

← Group #101535

Character table — Group #101535

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444422444444224444888888882244448888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111-1-11-1-111111-1-1-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-11-1-111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ711111111111111111111-1-11-1-11-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-1-1-1
χ811111111111111111111-1-11-1-11-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ911111111-1-1-1-1111-1-1-1-1111-1-1-11ii−i−iii−i−i111-1-1-1i−ii−iii−i−iii−i−i11-1-1
χ1011111111-1-1-1-1111-1-1-1-1111-1-1-11ii−i−iii−i−i-1-11-111i−ii−i−i−iii−i−iii-1-111
χ1111111111-1-1-1-1111-1-1-1-1111-1-1-11−i−iii−i−iii111-1-1-1−ii−ii−i−iii−i−iii11-1-1
χ1211111111-1-1-1-1111-1-1-1-1111-1-1-11−i−iii−i−iii-1-11-111−ii−iiii−i−iii−i−i-1-111
χ1311111111-1-1-1-1111-1-1-1-11-1-1-1111ii−i−i−i−iii11-11-1-1i−i−iiii−i−i−i−iii-1-111
χ1411111111-1-1-1-1111-1-1-1-11-1-1-1111ii−i−i−i−iii-1-1-1111i−i−ii−i−iiiii−i−i11-1-1
χ1511111111-1-1-1-1111-1-1-1-11-1-1-1111−i−iiiii−i−i11-11-1-1−iii−i−i−iiiii−i−i-1-111
χ1611111111-1-1-1-1111-1-1-1-11-1-1-1111−i−iiiii−i−i-1-1-1111−iii−iii−i−i−i−iii11-1-1
χ1722222222222222-2-2-222-200-200-20000222200000000-2-2000000000000
χ1822222222222222-2-2-222-200-200-20000-2-2-2-20000000022000000000000
χ19222222222222-2-22-2-2-2-2222222-20000000000-2-2000000000000000000
χ20222222222222-2-22-2-2-2-22-2-22-2-2-2000000000022000000000000000000
χ21222222222222-2-2-222-2-2-200-200222220000000000-2-200000000000000
χ22222222222222-2-2-222-2-2-200-2002-2-2-2-200000000002200000000000000
χ2322222222-2-2-2-222-222-2-2-200200-200002i2i−2i−2i00000000−2i2i000000000000
χ2422222222-2-2-2-222-222-2-2-200200-20000−2i−2i2i2i000000002i−2i000000000000
χ2522222222-2-2-2-2-2-222222222-2-2-2-20000000000-22000000000000000000
χ2622222222-2-2-2-2-2-2222222-2-2-222-200000000002-2000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-222-20020022i2i−2i−2i0000000000−2i2i00000000000000
χ2822222222-2-2-2-2-2-2-2-2-222-2002002−2i−2i2i2i00000000002i−2i00000000000000
χ2922-222-2-2-22i2i−2i−2i2-20002i−2i000000000002ζ−2ζ2ζ3−2ζ300000000001+i−1−i1−i−1+i00002−2i2−i2
χ3022-222-2-2-22i2i−2i−2i2-20002i−2i000000000002ζ−2ζ2ζ3−2ζ30000000000−1−i1+i−1+i1−i0000−22−i2i2
χ3122-222-2-2-22i2i−2i−2i2-20002i−2i00000000000−2ζ2ζ−2ζ32ζ300000000001+i−1−i1−i−1+i0000−22−i2i2
χ3222-222-2-2-22i2i−2i−2i2-20002i−2i00000000000−2ζ2ζ−2ζ32ζ30000000000−1−i1+i−1+i1−i00002−2i2−i2
χ3322-222-2-2-2−2i−2i2i2i2-2000−2i2i000000000002ζ3−2ζ32ζ−2ζ00000000001−i−1+i1+i−1−i0000−22i2−i2
χ3422-222-2-2-2−2i−2i2i2i2-2000−2i2i000000000002ζ3−2ζ32ζ−2ζ0000000000−1+i1−i−1−i1+i00002−2−i2i2
χ3522-222-2-2-2−2i−2i2i2i2-2000−2i2i00000000000−2ζ32ζ3−2ζ2ζ00000000001−i−1+i1+i−1−i00002−2−i2i2
χ3622-222-2-2-2−2i−2i2i2i2-2000−2i2i00000000000−2ζ32ζ3−2ζ2ζ0000000000−1+i1−i−1−i1+i0000−22i2−i2
χ37444-4-4-44-400000004i−4i0000000002+2i−2−2i2−2i−2+2i00000000000000000000000000
χ38444-4-4-44-400000004i−4i000000000−2−2i2+2i−2+2i2−2i00000000000000000000000000
χ39444-4-4-44-40000000−4i4i0000000002−2i−2+2i2+2i−2−2i00000000000000000000000000
χ40444-4-4-44-40000000−4i4i000000000−2+2i2−2i−2−2i2+2i00000000000000000000000000
χ4144-444-4-4-44i4i−4i−4i-44000−4i4i0000000000000000000000000000000000000
χ4244-444-4-4-4−4i−4i4i4i-440004i−4i0000000000000000000000000000000000000
χ434-444-44-4-44i−4i4i−4i0000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ444-444-44-4-44i−4i4i−4i000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ454-444-44-4-4−4i4i−4i4i0000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ464-444-44-4-4−4i4i−4i4i000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ474-44-44-4-4400000040000-40004i−4i0000000000000000000000000000000
χ484-44-44-4-4400000040000-4000−4i4i0000000000000000000000000000000
χ494-44-44-4-44000000-4000044-40000000000000000000000000000000000
χ504-44-44-4-44000000-400004-440000000000000000000000000000000000
χ514-4-44-4-4444-4-4400000000000000000000002-2002-20000000000000000
χ524-4-44-4-4444-4-440000000000000000000000-2200-220000000000000000
χ534-4-44-4-444-444-400000000000000000000002-200-220000000000000000
χ544-4-44-4-444-444-40000000000000000000000-22002-20000000000000000
χ5588-8-8-88-88000000000000000000000000000000000000000000000000
χ568-8-8-8888-8000000000000000000000000000000000000000000000000

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