Finite Group Databasebeta

← Group #98710

Character table — Group #98710

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444422224444444488888888444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ911111111-1-1-1-111-11111-1-1-1-1-111-1-1111111-1-1iiii−i−i−i−i1-1-1-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-11111-1-1-1-1-111-1-1111111-1-1−i−i−i−iiiii1-1-1-11-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-111-11111-1-1-1-1-111-1-1-1-1-1-1-1-111iiii−i−i−i−i1-111-11−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-111-11111-1-1-1-1-111-1-1-1-1-1-1-1-111−i−i−i−iiiii1-111-11ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-111-11111-1-1-1-1-1-1-1111111-1-111iiii−i−i−i−i-11-1-1-11ii−i−i−i−iii−i−iii
χ1411111111-1-1-1-111-11111-1-1-1-1-1-1-1111111-1-111−i−i−i−iiiii-11-1-1-11−i−iiiii−i−iii−i−i
χ1511111111-1-1-1-111-11111-1-1-1-1-1-1-111-1-1-1-111-1-1iiii−i−i−i−i-11111-1−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-111-11111-1-1-1-1-1-1-111-1-1-1-111-1-1−i−i−i−iiiii-11111-1ii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-2-2-222-2-2000022-2-2000000000000002-200000000000000
χ1822222222222222-2-2-2-2-2-222-2-20000-2-22200000000000000-2200000000000000
χ19222222222222-2-2222-2-2-2-2-22-2000000002222000000000000-2-2000000000000
χ20222222222222-2-2222-2-2-2-2-22-200000000-2-2-2-200000000000022000000000000
χ21222222222222-2-2-2-2-2222-2-2-2222220000000000000000-2-20000000000000000
χ22222222222222-2-2-2-2-2222-2-2-22-2-2-2-20000000000000000220000000000000000
χ2322222222-2-2-2-2222-2-2-2-22-2-222000022-2-200000000000000-2200000000000000
χ2422222222-2-2-2-2222-2-2-2-22-2-2220000-2-222000000000000002-200000000000000
χ2522222222-2-2-2-2-2-22-2-222-2222-222-2-20000000000000000-220000000000000000
χ2622222222-2-2-2-2-2-22-2-222-2222-2-2-22200000000000000002-20000000000000000
χ2722222222-2-2-2-2-2-2-222-2-2222-220000000022-2-2000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-222-2-2222-2200000000-2-2220000000000002-2000000000000
χ2922-2-222-2-222-2-200-22-20000020000000002i−2i2i−2i22−2−222−2−200000000000000i2−i2i2−i2
χ3022-2-222-2-222-2-200-22-20000020000000002i−2i2i−2i−2−222−2−22200000000000000−i2i2−i2i2
χ3122-2-222-2-222-2-200-22-2000002000000000−2i2i−2i2i22−2−222−2−200000000000000−i2i2−i2i2
χ3222-2-222-2-222-2-200-22-2000002000000000−2i2i−2i2i−2−222−2−22200000000000000i2−i2i2−i2
χ3322-2-222-2-2-2-2220022-200000-20000000002i−2i−2i2ii2i2−i2−i2−i2−i2i2i200000000000000−222−2
χ3422-2-222-2-2-2-2220022-200000-20000000002i−2i−2i2i−i2−i2i2i2i2i2−i2−i2000000000000002−2−22
χ3522-2-222-2-2-2-2220022-200000-2000000000−2i2i2i−2ii2i2−i2−i2−i2−i2i2i2000000000000002−2−22
χ3622-2-222-2-2-2-2220022-200000-2000000000−2i2i2i−2i−i2−i2i2i2i2i2−i2−i200000000000000−222−2
χ372-2-2-22-2222-22-2000002-22000-22-22-200000000i2−i2i2−i2i2−i2i2−i20000000000i2−i2i2−i20000
χ382-2-2-22-2222-22-2000002-22000-22-22-200000000−i2i2−i2i2−i2i2−i2i20000000000−i2i2−i2i20000
χ392-2-2-22-2222-22-2000002-22000-2-22-2200000000i2−i2i2−i2i2−i2i2−i20000000000−i2i2−i2i20000
χ402-2-2-22-2222-22-2000002-22000-2-22-2200000000−i2i2−i2i2−i2i2−i2i20000000000i2−i2i2−i20000
χ412-2-2-22-222-22-22000002-2-200022-2-22000000002−22−2−22−2200000000002−2−220000
χ422-2-2-22-222-22-22000002-2-200022-2-2200000000−22−222−22−20000000000−222−20000
χ432-2-2-22-222-22-22000002-2-20002-222-2000000002−22−2−22−220000000000−222−20000
χ442-2-2-22-222-22-22000002-2-20002-222-200000000−22−222−22−200000000002−2−220000
χ45444-4-4-4-440000000000004i−4i00000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ46444-4-4-4-440000000000004i−4i0000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ47444-4-4-4-44000000000000−4i4i00000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ48444-4-4-4-44000000000000−4i4i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ4944-4-444-4-444-4-4004-4400000-4000000000000000000000000000000000000000
χ5044-4-444-4-4-4-44400-4-44000004000000000000000000000000000000000000000
χ514-4444-4-4-44-4-440000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ524-4444-4-4-44-4-44000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ534-4444-4-4-4-444-40000000000000000000000002-2-22-222-2000000000000000000
χ544-4444-4-4-4-444-4000000000000000000000000-222-22-2-22000000000000000000
χ554-44-4-444-400004-400000000000000004i−4i000000000000000000000000000000
χ564-44-4-444-400004-40000000000000000−4i4i000000000000000000000000000000
χ574-44-4-444-40000-44000000000000004i−4i00000000000000000000000000000000
χ584-44-4-444-40000-4400000000000000−4i4i00000000000000000000000000000000
χ594-4-4-44-4444-44-400000-44-4000400000000000000000000000000000000000000
χ604-4-4-44-444-44-4400000-444000-400000000000000000000000000000000000000
χ6188-88-8-88-8000000000000000000000000000000000000000000000000000000
χ628-8-88-88-88000000000000000000000000000000000000000000000000000000

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