Finite Group Databasebeta

← Group #98585

Character table — Group #98585

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444422444444444444444444444488888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1111111111-11-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-11-11-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-11-1-111111111-1-1-1-1
χ911111111-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1iiii−i−i−i−i-111-1-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1-1-1111111-1-1-1-111-1-1111111-1-1−i−i−i−iiiii-111-1-1-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111iiii−i−i−i−i-1-11111ii−i−i−i−iii−i−iii
χ1211111111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-111−i−i−i−iiiii-1-11111−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111iiii−i−i−i−i1-1-11-1-1−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-111−i−i−i−iiiii1-1-11-1-1ii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−i11-1-111−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii11-1-111ii−i−iii−i−i−i−iii
χ1722222222222222-2-222-2-2-2-2-2-2000000002222000000000-20-200000000000000
χ1822222222222222-2-222-2-2-2-2-2-200000000-2-2-2-200000000020200000000000000
χ19222222222222-2-222-2-2-2-2-2-222000022-2-200000000000000002-2000000000000
χ20222222222222-2-222-2-2-2-2-2-2220000-2-2220000000000000000-22000000000000
χ21222222222222-2-2-2-2-2-22222-2-222220000000000000000-20-2000000000000000
χ22222222222222-2-2-2-2-2-22222-2-2-2-2-2-20000000000000000202000000000000000
χ2322222222-2-2-2-22222-2-2-2-222-2-2000022-2-20000000000000000-22000000000000
χ2422222222-2-2-2-22222-2-2-2-222-2-20000-2-22200000000000000002-2000000000000
χ2522222222-2-2-2-222-2-2-2-222-2-22222-2-2000000000000000020-2000000000000000
χ2622222222-2-2-2-222-2-2-2-222-2-222-2-2220000000000000000-202000000000000000
χ2722222222-2-2-2-2-2-2-2-222-2-222220000000022-2-2000000000-20200000000000000
χ2822222222-2-2-2-2-2-2-2-222-2-2222200000000-2-22200000000020-200000000000000
χ2922-222-2-2-222-2-2-22002-2000000000000002i−2i2i−2i22−2−222−2−200000000000000i2−i2i2−i2
χ3022-222-2-2-222-2-2-22002-2000000000000002i−2i2i−2i−2−222−2−22200000000000000−i2i2−i2i2
χ3122-222-2-2-222-2-2-22002-200000000000000−2i2i−2i2i22−2−222−2−200000000000000−i2i2−i2i2
χ3222-222-2-2-222-2-2-22002-200000000000000−2i2i−2i2i−2−222−2−22200000000000000i2−i2i2−i2
χ3322-222-2-2-2-2-2222-2002-2000000000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i200000000000000−222−2
χ3422-222-2-2-2-2-2222-2002-2000000000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2000000000000002−2−22
χ3522-222-2-2-2-2-2222-2002-200000000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2000000000000002−2−22
χ3622-222-2-2-2-2-2222-2002-200000000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i200000000000000−222−2
χ3722-2-2-222-22i−2i2i−2i0000002-22i−2i002-22i−2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000001+i−1−i1−i−1+i00000000
χ3822-2-2-222-22i−2i2i−2i0000002-22i−2i002-22i−2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000−1−i1+i−1+i1−i00000000
χ3922-2-2-222-22i−2i2i−2i0000002-22i−2i00-22−2i2i000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i000000−1−i1+i−1+i1−i00000000
χ4022-2-2-222-22i−2i2i−2i0000002-22i−2i00-22−2i2i00000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000001+i−1−i1−i−1+i00000000
χ4122-2-2-222-2−2i2i−2i2i0000002-2−2i2i002-2−2i2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000001−i−1+i1+i−1−i00000000
χ4222-2-2-222-2−2i2i−2i2i0000002-2−2i2i002-2−2i2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000−1+i1−i−1−i1+i00000000
χ4322-2-2-222-2−2i2i−2i2i0000002-2−2i2i00-222i−2i000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i000000−1+i1−i−1−i1+i00000000
χ4422-2-2-222-2−2i2i−2i2i0000002-2−2i2i00-222i−2i00000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000001−i−1+i1+i−1−i00000000
χ45444-4-4-4-444i−4i−4i4i0000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000
χ46444-4-4-4-444i−4i−4i4i000000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000
χ47444-4-4-4-44−4i4i4i−4i0000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000
χ48444-4-4-4-44−4i4i4i−4i000000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000
χ4944-444-4-4-444-4-44-400-4400000000000000000000000000000000000000000000
χ5044-444-4-4-4-4-444-4400-4400000000000000000000000000000000000000000000
χ5144-4-4-444-44i−4i4i−4i000000-44−4i4i0000000000000000000000000000000000000000
χ5244-4-4-444-4−4i4i−4i4i000000-444i−4i0000000000000000000000000000000000000000
χ534-444-44-4-40000004-4000000000000004i−4i000000000000000000000000000000
χ544-444-44-4-40000004-400000000000000−4i4i000000000000000000000000000000
χ554-444-44-4-4000000-440000000000004i−4i00000000000000000000000000000000
χ564-444-44-4-4000000-44000000000000−4i4i00000000000000000000000000000000
χ574-44-44-44-4000000000000004i−4i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ30000
χ584-44-44-44-4000000000000004i−4i000000000000000000000000000000−2ζ2ζ−2ζ32ζ30000
χ594-44-44-44-400000000000000−4i4i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ0000
χ604-44-44-44-400000000000000−4i4i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ0000
χ618-8-88-8-888000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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