Finite Group Databasebeta

← Group #98644

Character table — Group #98644

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444444444444444488888888444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1111111111-1-11-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-111111111-1-1-1-1
χ911111111-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1iiii−i−i−i−i11-1-1-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-1−i−i−i−iiiii11-1-1-1-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111iiii−i−i−i−i1-11-111−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-111−i−i−i−iiiii1-11-111ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111iiii−i−i−i−i-1-111-1-1ii−i−i−i−iii−i−iii
χ1411111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111−i−i−i−iiiii-1-111-1-1−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−i-11-1111−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii-11-1111ii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-222-2-2-2-2000022-2-200000000000000002-2000000000000
χ1822222222222222-2-2-2-222-2-2-2-20000-2-2220000000000000000-22000000000000
χ19222222222222-2-222-2-2-2-222-2-222220000000000000000-200-200000000000000
χ20222222222222-2-222-2-2-2-222-2-2-2-2-2-20000000000000000200200000000000000
χ21222222222222-2-2-2-222-2-2-2-222000000002222000000000-2-2000000000000000
χ22222222222222-2-2-2-222-2-2-2-22200000000-2-2-2-200000000022000000000000000
χ2322222222-2-2-2-222-2-2-2-2-2-22222000022-2-20000000000000000-22000000000000
χ2422222222-2-2-2-222-2-2-2-2-2-222220000-2-22200000000000000002-2000000000000
χ2522222222-2-2-2-2-2-222-2-222-2-22222-2-20000000000000000-200200000000000000
χ2622222222-2-2-2-2-2-222-2-222-2-222-2-2220000000000000000200-200000000000000
χ2722222222-2-2-2-2-2-2-2-2222222-2-20000000022-2-2000000000-22000000000000000
χ2822222222-2-2-2-2-2-2-2-2222222-2-200000000-2-2220000000002-2000000000000000
χ2922-22-2-2-222i−2i2i−2i002-200002i−2i002-22i−2i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000001+i−1−i1−i−1+i0000
χ3022-22-2-2-222i−2i2i−2i002-200002i−2i002-22i−2i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−1−i1+i−1+i1−i0000
χ3122-22-2-2-222i−2i2i−2i002-200002i−2i00-22−2i2i000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−1−i1+i−1+i1−i0000
χ3222-22-2-2-222i−2i2i−2i002-200002i−2i00-22−2i2i00000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000001+i−1−i1−i−1+i0000
χ3322-22-2-2-22−2i2i−2i2i002-20000−2i2i002-2−2i2i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000001−i−1+i1+i−1−i0000
χ3422-22-2-2-22−2i2i−2i2i002-20000−2i2i002-2−2i2i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−1+i1−i−1−i1+i0000
χ3522-22-2-2-22−2i2i−2i2i002-20000−2i2i00-222i−2i000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−1+i1−i−1−i1+i0000
χ3622-22-2-2-22−2i2i−2i2i002-20000−2i2i00-222i−2i00000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000001−i−1+i1+i−1−i0000
χ372-2-2222-2-22i−2i−2i2i00002-200002i−2i000000002-22i−2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000001+i−1−i1−i−1+i
χ382-2-2222-2-22i−2i−2i2i00002-200002i−2i000000002-22i−2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000000000−1−i1+i−1+i1−i
χ392-2-2222-2-22i−2i−2i2i00002-200002i−2i00000000-22−2i2i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000000000−1−i1+i−1+i1−i
χ402-2-2222-2-22i−2i−2i2i00002-200002i−2i00000000-22−2i2i−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000001+i−1−i1−i−1+i
χ412-2-2222-2-2−2i2i2i−2i00002-20000−2i2i000000002-2−2i2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000001−i−1+i1+i−1−i
χ422-2-2222-2-2−2i2i2i−2i00002-20000−2i2i000000002-2−2i2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000000000−1+i1−i−1−i1+i
χ432-2-2222-2-2−2i2i2i−2i00002-20000−2i2i00000000-222i−2i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000000000−1+i1−i−1−i1+i
χ442-2-2222-2-2−2i2i2i−2i00002-20000−2i2i00000000-222i−2i−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000001−i−1+i1+i−1−i
χ45444-44-4-4-400004-400000000000000004-4000000000000000000000000000000
χ46444-44-4-4-400004-40000000000000000-44000000000000000000000000000000
χ47444-44-4-4-40000-44000000000000004-400000000000000000000000000000000
χ48444-44-4-4-40000-4400000000000000-4400000000000000000000000000000000
χ4944-44-4-4-444i−4i4i−4i00-440000−4i4i0000000000000000000000000000000000000000
χ5044-44-4-4-44−4i4i−4i4i00-4400004i−4i0000000000000000000000000000000000000000
χ514-444-4-44-444-4-40000000000000000000000002-2-222-2-22000000000000000000
χ524-444-4-44-444-4-4000000000000000000000000-222-2-222-2000000000000000000
χ534-444-4-44-4-4-4440000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ544-444-4-44-4-4-444000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ554-44-4-44-4400000000004i−4i0000000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ564-44-4-44-4400000000004i−4i000000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ574-44-4-44-440000000000−4i4i0000000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ584-44-4-44-440000000000−4i4i000000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ594-4-4444-4-44i−4i−4i4i0000-440000−4i4i00000000000000000000000000000000000000
χ604-4-4444-4-4−4i4i4i−4i0000-4400004i−4i00000000000000000000000000000000000000
χ6188-8-8-888-8000000000000000000000000000000000000000000000000000000
χ628-8-8-88-888000000000000000000000000000000000000000000000000000000

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