Finite Group Databasebeta

← Group #98690

Character table — Group #98690

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222244444444444488888888888888888888161616161616161616161616161616161616
order12222222444444444444444422222222222288888888444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
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
χ911111111-1-1-1-111-1-11111-1-1-1-1111111-1-111-1-1iiii−i−i−i−i-1-11-11-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-111-1-11111-1-1-1-1111111-1-111-1-1−i−i−i−iiiii-1-11-11-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-111iiii−i−i−i−i-1-1-11-11ii−i−i−i−iii−i−iii
χ1211111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-111−i−i−i−iiiii-1-1-11-11−i−iiiii−i−iii−i−i
χ1311111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111iiii−i−i−i−i111-1-11−i−iiiii−i−i−i−iii
χ1411111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-111−i−i−i−iiiii111-1-11ii−i−i−i−iiiii−i−i
χ1511111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1iiii−i−i−i−i11-111-1−i−iii−i−iiiii−i−i
χ1611111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1−i−i−i−iiiii11-111-1ii−i−iii−i−i−i−iii
χ1722222222222222-2-2-2-2-2-222-2-222-2-200000000000000002-20000000000000000
χ1822222222222222-2-2-2-2-2-222-2-2-2-2220000000000000000-220000000000000000
χ19222222222222-2-22-222-2-2-2-22-2000000002222000000000000-2-2000000000000
χ20222222222222-2-22-222-2-2-2-22-200000000-2-2-2-200000000000022000000000000
χ21222222222222-2-2-22-2-222-2-2-220000222200000000000000-2-200000000000000
χ22222222222222-2-2-22-2-222-2-2-220000-2-2-2-2000000000000002200000000000000
χ2322222222-2-2-2-22222-2-2-2-2-2-22222-2-20000000000000000-220000000000000000
χ2422222222-2-2-2-22222-2-2-2-2-2-222-2-22200000000000000002-20000000000000000
χ2522222222-2-2-2-2-2-22-2-2-222222-2000022-2-200000000000000-2200000000000000
χ2622222222-2-2-2-2-2-22-2-2-222222-20000-2-222000000000000002-200000000000000
χ2722222222-2-2-2-2-2-2-2222-2-222-220000000022-2-2000000000000-22000000000000
χ2822222222-2-2-2-2-2-2-2222-2-222-2200000000-2-2220000000000002-2000000000000
χ2922-2-2-222-222-2-20002002-2000-200002-22-20000i2i2−i2−i2i2i2−i2−i20000000000i2−i2i2−i20000
χ3022-2-2-222-222-2-20002002-2000-200002-22-20000−i2−i2i2i2−i2−i2i2i20000000000−i2i2−i2i20000
χ3122-2-2-222-222-2-20002002-2000-20000-22-220000i2i2−i2−i2i2i2−i2−i20000000000−i2i2−i2i20000
χ3222-2-2-222-222-2-20002002-2000-20000-22-220000−i2−i2i2i2−i2−i2i2i20000000000i2−i2i2−i20000
χ3322-2-2-222-2-2-222000-2002-2000200002-2-22000022−2−2−2−22200000000002−2−220000
χ3422-2-2-222-2-2-222000-2002-2000200002-2-220000−2−22222−2−20000000000−222−20000
χ3522-2-2-222-2-2-222000-2002-200020000-222-2000022−2−2−2−2220000000000−222−20000
χ3622-2-2-222-2-2-222000-2002-200020000-222-20000−2−22222−2−200000000002−2−220000
χ372-22-2-22-222-22-200202-20000-20000000002-22-2i2−i2i2−i2i2−i2i2−i200000000000000i2−i2i2−i2
χ382-22-2-22-222-22-200202-20000-20000000002-22-2−i2i2−i2i2−i2i2−i2i200000000000000−i2i2−i2i2
χ392-22-2-22-222-22-200202-20000-2000000000-22-22i2−i2i2−i2i2−i2i2−i200000000000000−i2i2−i2i2
χ402-22-2-22-222-22-200202-20000-2000000000-22-22−i2i2−i2i2−i2i2−i2i200000000000000i2−i2i2−i2
χ412-22-2-22-22-22-2200-202-2000020000000002-2-222−22−2−22−22000000000000002−2−22
χ422-22-2-22-22-22-2200-202-2000020000000002-2-22−22−222−22−200000000000000−222−2
χ432-22-2-22-22-22-2200-202-200002000000000-222-22−22−2−22−2200000000000000−222−2
χ442-22-2-22-22-22-2200-202-200002000000000-222-2−22−222−22−2000000000000002−2−22
χ454444-4-4-4-40000000000004i−4i00000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ464444-4-4-4-40000000000004i−4i0000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ474444-4-4-4-4000000000000−4i4i00000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ484444-4-4-4-4000000000000−4i4i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ4944-4-4-444-444-4-4000-400-44000400000000000000000000000000000000000000
χ5044-4-4-444-4-4-444000400-44000-400000000000000000000000000000000000000
χ514-44-4-44-444-44-400-40-4400004000000000000000000000000000000000000000
χ524-44-4-44-44-44-440040-440000-4000000000000000000000000000000000000000
χ534-4-4444-4-44-4-440000000000000000000000002-2-222-2-22000000000000000000
χ544-4-4444-4-44-4-44000000000000000000000000-222-2-222-2000000000000000000
χ554-4-4444-4-4-444-40000000000000000000000002i−2i−2i2i−2i2i2i−2i000000000000000000
χ564-4-4444-4-4-444-4000000000000000000000000−2i2i2i−2i2i−2i−2i2i000000000000000000
χ574-4-44-4-44400004-40000000000004-40000000000000000000000000000000000
χ584-4-44-4-44400004-4000000000000-440000000000000000000000000000000000
χ594-4-44-4-4440000-4400000000004-4000000000000000000000000000000000000
χ604-4-44-4-4440000-440000000000-44000000000000000000000000000000000000
χ6188-8-88-8-88000000000000000000000000000000000000000000000000000000
χ628-88-88-88-8000000000000000000000000000000000000000000000000000000

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