Finite Group Databasebeta

← Group #456785

Character table — Group #456785

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222222222888888888888888888888888161616161616161616161616161616161616
order12222222222244444444224444444444444488888888444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-111-1-1
χ311111111111111111111111111111111-1-1-1-11111-1-1-1-11-111-1-1-11-1-1-1-1-1-1-1-111
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-11-1-11-1-1-111-1-111-1-1-1-1
χ51111111111111111111111-1-111-1-1-1-1-1-1111111111111-11-1-11-1-1-1-1-1-1-1-1-11111
χ61111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-111-1-1-1111-1-11111-1-1
χ71111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1111111-1-111
χ81111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-1-1-1-1
χ911111111111111111111-1-111-1-111-1-1-1-11111111111111-1-1-1-1-1-11-1-11111-1-1-1-1
χ1011111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-111
χ1111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1-111-1-1
χ1211111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-111-1-1-1-1-1111111
χ1311111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-111-111-111-1-1-1-1-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111-1-111
χ1511111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-11111-1-1-1-1-1111111-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-1-1-111111-1-11111
χ1722222222-2-2-2-222-22-2-2-22002200-2-20000000022-2-200002000000-20000000000
χ1822222222-2-2-2-222-22-2-2-22002200-2-200000000-2-2220000-200000020000000000
χ1922222222-2-2-2-222-22-2-2-2200-2-200220000000022-2-20000-200000020000000000
χ2022222222-2-2-2-222-22-2-2-2200-2-2002200000000-2-22200002000000-20000000000
χ2122222222-2-2-2-2-2-22-2222-22200-2-20000000000000022-2-20200-20000000000000
χ2222222222-2-2-2-2-2-22-2222-22200-2-200000000000000-2-2220-20020000000000000
χ2322222222-2-2-2-2-2-22-2222-2-2-200220000000000000022-2-20-20020000000000000
χ2422222222-2-2-2-2-2-22-2222-2-2-2002200000000000000-2-2220200-20000000000000
χ25222-2-22-2-22-2-222-2-2-222-22000000002i2i−2i−2i00000000000000000000002i−2i002-200
χ26222-2-22-2-22-2-222-2-2-222-22000000002i2i−2i−2i0000000000000000000000−2i2i00-2200
χ27222-2-22-2-22-2-222-2-2-222-2200000000−2i−2i2i2i00000000000000000000002i−2i00-2200
χ28222-2-22-2-22-2-222-2-2-222-2200000000−2i−2i2i2i0000000000000000000000−2i2i002-200
χ292-2-22-22-2222-2-222-2-22-22-22-22i−2i2-22i−2i2i−2i2i−2i000000000000000000000000000000
χ302-2-22-22-2222-2-222-2-22-22-22-2−2i2i2-2−2i2i−2i2i−2i2i000000000000000000000000000000
χ312-2-22-22-2222-2-222-2-22-22-2-222i−2i-222i−2i−2i2i−2i2i000000000000000000000000000000
χ322-2-22-22-2222-2-222-2-22-22-2-22−2i2i-22−2i2i2i−2i2i−2i000000000000000000000000000000
χ332-2-22-22-22-2-222222-2-22-2-2002i−2i00−2i2i0000000000000000002-20000000000002i−2i
χ342-2-22-22-22-2-222222-2-22-2-2002i−2i00−2i2i000000000000000000-22000000000000−2i2i
χ352-2-22-22-22-2-222222-2-22-2-200−2i2i002i−2i0000000000000000002-2000000000000−2i2i
χ362-2-22-22-22-2-222222-2-22-2-200−2i2i002i−2i000000000000000000-220000000000002i−2i
χ372-2-22-22-22-2-222-2-2-222-2222-200-22000000000000000000000000002-2002-20000
χ382-2-22-22-22-2-222-2-2-222-2222-200-2200000000000000000000000000-2200-220000
χ392-2-22-22-22-2-222-2-2-222-222-22002-2000000000000000000000000002-200-220000
χ402-2-22-22-22-2-222-2-2-222-222-22002-200000000000000000000000000-22002-20000
χ412-2-2-2222-22-22-22-2222-2-2-2000000002-2-222i2i−2i−2i00000000000002i−2i00000000000
χ422-2-2-2222-22-22-22-2222-2-2-2000000002-2-22−2i−2i2i2i0000000000000−2i2i00000000000
χ432-2-2-2222-22-22-22-2222-2-2-200000000-222-22i2i−2i−2i0000000000000−2i2i00000000000
χ442-2-2-2222-22-22-22-2222-2-2-200000000-222-2−2i−2i2i2i00000000000002i−2i00000000000
χ45444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000
χ46444-4-44-4-44-4-44-4444-4-44-4000000000000000000000000000000000000000000
χ47444-4-44-4-4-444-44-44-4-4-444000000000000000000000000000000000000000000
χ48444-4-44-4-4-444-4-44-4444-4-4000000000000000000000000000000000000000000
χ4944-444-4-4-40000000000000000000000002-22-222−220022−2200000000000000000000
χ5044-444-4-4-40000000000000000000000002-22-2−222200−222200000000000000000000
χ5144-444-4-4-4000000000000000000000000-22-2222−2200−222200000000000000000000
χ5244-444-4-4-4000000000000000000000000-22-22−22220022−2200000000000000000000
χ534-44-44-4-440000000000000000000000002i−2i−2i2i0022−22002i2−2i2000000000000000000
χ544-44-44-4-440000000000000000000000002i−2i−2i2i00−222200−2i22i2000000000000000000
χ554-44-44-4-44000000000000000000000000−2i2i2i−2i0022−2200−2i22i2000000000000000000
χ564-44-44-4-44000000000000000000000000−2i2i2i−2i00−2222002i2−2i2000000000000000000
χ574-4-44-44-4444-4-4-4-444-44-44000000000000000000000000000000000000000000
χ584-4-4-4444-44-44-4-44-4-4-4444000000000000000000000000000000000000000000
χ594-4-4-4444-4-44-444-4-44-444-4000000000000000000000000000000000000000000
χ604-4-4-4444-4-44-44-444-44-4-44000000000000000000000000000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-888-8-88-8000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).