Finite Group Databasebeta

← Group #98714

Character table — Group #98714

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
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111
χ911111111-1-1-1-11111-111-1-1-1-1-111-1-111-1-11111iiii−i−i−i−i1-11-1-1-1ii−i−iii−i−iii−i−i
χ1011111111-1-1-1-11111-111-1-1-1-1-111-1-111-1-11111−i−i−i−iiiii1-11-1-1-1−i−iii−i−iii−i−iii
χ1111111111-1-1-1-11111-111-1-1-1-1-111-1-1-1-111-1-1-1-1iiii−i−i−i−i-111-111−i−iiiii−i−i−i−iii
χ1211111111-1-1-1-11111-111-1-1-1-1-111-1-1-1-111-1-1-1-1−i−i−i−iiiii-111-111ii−i−i−i−iiiii−i−i
χ1311111111-1-1-1-11111-111-1-1-1-1-1-1-11111-1-1-1-1-1-1iiii−i−i−i−i1-1-1111−i−iii−i−iiiii−i−i
χ1411111111-1-1-1-11111-111-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−i−i−iiiii1-1-1111ii−i−iii−i−i−i−iii
χ1511111111-1-1-1-11111-111-1-1-1-1-1-1-111-1-1111111iiii−i−i−i−i-11-11-1-1ii−i−i−i−iii−i−iii
χ1611111111-1-1-1-11111-111-1-1-1-1-1-1-111-1-1111111−i−i−i−iiiii-11-11-1-1−i−iiiii−i−iii−i−i
χ1722222222222222-2-22-2-2-2-2-22-22222000000000000000000-2-200000000000000
χ1822222222222222-2-22-2-2-2-2-22-2-2-2-2-20000000000000000002200000000000000
χ19222222222222-2-222-2-2-2-222-2-20000000022-2-20000000000002-2000000000000
χ20222222222222-2-222-2-2-2-222-2-200000000-2-222000000000000-22000000000000
χ21222222222222-2-2-2-2-2222-2-2-2200002222000000000000-2-20000000000000000
χ22222222222222-2-2-2-2-2222-2-2-220000-2-2-2-2000000000000220000000000000000
χ2322222222-2-2-2-222-2-2-2-2-2222-2222-2-2000000000000000000-2200000000000000
χ2422222222-2-2-2-222-2-2-2-2-2222-22-2-2220000000000000000002-200000000000000
χ2522222222-2-2-2-2-2-2222-2-22-2-2220000000022-2-2000000000000-22000000000000
χ2622222222-2-2-2-2-2-2222-2-22-2-22200000000-2-2220000000000002-2000000000000
χ2722222222-2-2-2-2-2-2-2-2222-2222-2000022-2-2000000000000-220000000000000000
χ2822222222-2-2-2-2-2-2-2-2222-2222-20000-2-2220000000000002-20000000000000000
χ292222-2-2-2-222-2-22-200200000-202-22-20000000022−2−222−2−200000000002−22−20000
χ302222-2-2-2-222-2-22-200200000-202-22-200000000−2−222−2−2220000000000−22−220000
χ312222-2-2-2-222-2-22-200200000-20-22-220000000022−2−222−2−20000000000−22−220000
χ322222-2-2-2-222-2-22-200200000-20-22-2200000000−2−222−2−22200000000002−22−20000
χ332222-2-2-2-2-2-2222-200-200000202-2-2200000000i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i20000
χ342222-2-2-2-2-2-2222-200-200000202-2-2200000000−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i20000
χ352222-2-2-2-2-2-2222-200-20000020-222-200000000i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i20000
χ362222-2-2-2-2-2-2222-200-20000020-222-200000000−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i20000
χ3722-2-2-2-2222-22-2000002-22000-200002-22-20000i2−i2i2−i2i2−i2i2−i200000000000000i2−i2i2−i2
χ3822-2-2-2-2222-22-2000002-22000-200002-22-20000−i2i2−i2i2−i2i2−i2i200000000000000−i2i2−i2i2
χ3922-2-2-2-2222-22-2000002-22000-20000-22-220000i2−i2i2−i2i2−i2i2−i200000000000000−i2i2−i2i2
χ4022-2-2-2-2222-22-2000002-22000-20000-22-220000−i2i2−i2i2−i2i2−i2i200000000000000i2−i2i2−i2
χ4122-2-2-2-222-22-22000002-2-2000200002-2-2200002−22−2−22−22000000000000002−2−22
χ4222-2-2-2-222-22-22000002-2-2000200002-2-220000−22−222−22−200000000000000−222−2
χ4322-2-2-2-222-22-22000002-2-200020000-222-200002−22−2−22−2200000000000000−222−2
χ4422-2-2-2-222-22-22000002-2-200020000-222-20000−22−222−22−2000000000000002−2−22
χ454444-4-4-4-444-4-4-4400-4000004000000000000000000000000000000000000000
χ464444-4-4-4-4-4-444-4400400000-4000000000000000000000000000000000000000
χ4744-4-444-4-44-4-440000000000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ4844-4-444-4-44-4-44000000000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ4944-4-444-4-4-444-40000000000000000000000002-2-22-222-2000000000000000000
χ5044-4-444-4-4-444-4000000000000000000000000-222-22-2-22000000000000000000
χ5144-4-4-4-4444-44-400000-44-4000400000000000000000000000000000000000000
χ5244-4-4-4-444-44-4400000-444000-400000000000000000000000000000000000000
χ534-44-44-44-40000004-40000000000000000004i−4i00000000000000000000000000
χ544-44-44-44-40000004-4000000000000000000−4i4i00000000000000000000000000
χ554-44-44-44-4000000-4400000000000000004i−4i0000000000000000000000000000
χ564-44-44-44-4000000-440000000000000000−4i4i0000000000000000000000000000
χ574-4-444-4-440000000000004i−4i00000000000000000000000000002ζ−2ζ2ζ3−2ζ300000000
χ584-4-444-4-440000000000004i−4i0000000000000000000000000000−2ζ2ζ−2ζ32ζ300000000
χ594-4-444-4-44000000000000−4i4i00000000000000000000000000002ζ3−2ζ32ζ−2ζ00000000
χ604-4-444-4-44000000000000−4i4i0000000000000000000000000000−2ζ32ζ3−2ζ2ζ00000000
χ618-88-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-88-888-8000000000000000000000000000000000000000000000000000000

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