Finite Group Databasebeta

← Group #98079

Character table — Group #98079

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size111111112222444444448888888888888816161616161616161616161616161616161616161616
order12222222444422444444224444888888884444444444444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111
χ511111111111111111111-1-111-1-1111111111-1-1-11-11-11-11111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-111-1-111111111-11-1-1-11-11-11-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11-1-1-11-11-11-1-1-1-1-111111111
χ811111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11-1111111111-1-1-1-1
χ911111111-1-1-1-1-1-111-1-1-1-11111-1-1iiii−i−i−i−i1-11-1-1111-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-111-1-1-1-11111-1-1iiii−i−i−i−i-111-11-1-1-111−i−iiiii−i−i−i−iii
χ1111111111-1-1-1-1-1-111-1-1-1-11111-1-1−i−i−i−iiiii1-11-1-1111-1-1−i−iii−i−iii−i−iii
χ1211111111-1-1-1-1-1-111-1-1-1-11111-1-1−i−i−i−iiiii-111-11-1-1-111ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-1-1-111-1-1-1-1-1-11111iiii−i−i−i−i11-11-1-11-1-11ii−i−i−i−iii−i−iii
χ1411111111-1-1-1-1-1-111-1-1-1-1-1-11111iiii−i−i−i−i-1-1-1111-111-1−i−iii−i−iiiii−i−i
χ1511111111-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−iiiii11-11-1-11-1-11−i−iiiii−i−iii−i−i
χ1611111111-1-1-1-1-1-111-1-1-1-1-1-11111−i−i−i−iiiii-1-1-1111-111-1ii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-2-2-200-2200000000000200020-20-2000000000000
χ1822222222222222-2-2-2-2-2-200-2200000000000-2000-20202000000000000
χ19222222222222-2-22222-2-222-2-2220000000000-2-2000000000000000000
χ20222222222222-2-22222-2-2-2-2-2-2-2-2000000000022000000000000000000
χ21222222222222-2-2-2-2-2-222002-20000000000200020-20-20000000000000
χ22222222222222-2-2-2-2-2-222002-20000000000-2000-202020000000000000
χ2322222222-2-2-2-22222-2-22222-2-2-2-20000000000-22000000000000000000
χ2422222222-2-2-2-22222-2-222-2-2-2-22200000000002-2000000000000000000
χ2522222222-2-2-2-222-2-222-2-2002-200000000002000-20-2020000000000000
χ2622222222-2-2-2-222-2-222-2-2002-20000000000-20002020-20000000000000
χ2722222222-2-2-2-2-2-2-2-2222200-22000000000002000-2020-2000000000000
χ2822222222-2-2-2-2-2-2-2-2222200-2200000000000-200020-202000000000000
χ2922-2-22-22-22i−2i2i−2i002-22i−2i002-2002i−2i0000000000000000001+i−1−i1−i−1+i00001+i−1−i1−i−1+i
χ3022-2-22-22-22i−2i2i−2i002-22i−2i002-2002i−2i000000000000000000−1−i1+i−1+i1−i0000−1−i1+i−1+i1−i
χ3122-2-22-22-22i−2i2i−2i002-22i−2i00-2200−2i2i0000000000000000001+i−1−i1−i−1+i0000−1−i1+i−1+i1−i
χ3222-2-22-22-22i−2i2i−2i002-22i−2i00-2200−2i2i000000000000000000−1−i1+i−1+i1−i00001+i−1−i1−i−1+i
χ3322-2-22-22-2−2i2i−2i2i002-2−2i2i002-200−2i2i0000000000000000001−i−1+i1+i−1−i00001−i−1+i1+i−1−i
χ3422-2-22-22-2−2i2i−2i2i002-2−2i2i002-200−2i2i000000000000000000−1+i1−i−1−i1+i0000−1+i1−i−1−i1+i
χ3522-2-22-22-2−2i2i−2i2i002-2−2i2i00-22002i−2i0000000000000000001−i−1+i1+i−1−i0000−1+i1−i−1−i1+i
χ3622-2-22-22-2−2i2i−2i2i002-2−2i2i00-22002i−2i000000000000000000−1+i1−i−1−i1+i00001−i−1+i1+i−1−i
χ37444-4-4-4-4400000000004i−4i0000002ζ2ζ−2ζ−2ζ2ζ32ζ3−2ζ3−2ζ30000000000000000000000
χ38444-4-4-4-4400000000004i−4i000000−2ζ−2ζ2ζ2ζ−2ζ3−2ζ32ζ32ζ30000000000000000000000
χ39444-4-4-4-440000000000−4i4i0000002ζ32ζ3−2ζ3−2ζ32ζ2ζ−2ζ−2ζ0000000000000000000000
χ40444-4-4-4-440000000000−4i4i000000−2ζ3−2ζ32ζ32ζ3−2ζ−2ζ2ζ2ζ0000000000000000000000
χ4144-4-44-44-44i−4i4i−4i00-44−4i4i00000000000000000000000000000000000000
χ4244-4-44-44-4−4i4i−4i4i00-444i−4i00000000000000000000000000000000000000
χ434-4444-4-4-400004-40000000000002-22-22-22-20000000000000000000000
χ444-4444-4-4-400004-4000000000000-22-22-22-220000000000000000000000
χ454-4444-4-4-40000-440000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000
χ464-4444-4-4-40000-44000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000
χ474-44-4-444-44i−4i−4i4i000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ484-44-4-444-44i−4i−4i4i00000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ494-44-4-444-4−4i4i4i−4i000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ504-44-4-444-4−4i4i4i−4i00000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ514-4-44-4-44444-4-40000000000000000000000000000000000002i−2i2i−2i0000
χ524-4-44-4-44444-4-4000000000000000000000000000000000000−2i2i−2i2i0000
χ534-4-44-4-444-4-4440000000000000000000000000000000000002-2-220000
χ544-4-44-4-444-4-444000000000000000000000000000000000000-222-20000
χ5588-88-88-8-8000000000000000000000000000000000000000000000000
χ568-8-8-888-88000000000000000000000000000000000000000000000000

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