Finite Group Databasebeta

← Group #428394

Character table — Group #428394

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222888888888888888888888888888888888888161616161616161616161616
order12222222222244444444224444444444444444444444444488888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-111-1-1-1-111
χ51111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ911111111111111111111-1-1111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ1011111111111111111111-1-111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111
χ1111111111111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111
χ1211111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1311111111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111-1-111
χ1411111111111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-11111
χ1722222222-2-2-2-222-2-22-22-200000022-2-2000022-2-20000000000000022-2-2000000000000
χ1822222222-2-2-2-222-2-22-22-200000022-2-20000-2-22200000000000000-2-222000000000000
χ1922222222-2-2-2-222-2-22-22-2000000-2-222000022-2-200000000000000-2-222000000000000
χ2022222222-2-2-2-222-2-22-22-2000000-2-2220000-2-2220000000000000022-2-2000000000000
χ2122222222-2-2-2-2-2-222-22-222222-2-2000000000000-2-20000000022-2-20000000000000000
χ2222222222-2-2-2-2-2-222-22-2222-2-222000000000000-2-200000000-2-2220000000000000000
χ2322222222-2-2-2-2-2-222-22-22-2-222-2-20000000000002200000000-2-2220000000000000000
χ2422222222-2-2-2-2-2-222-22-22-2-2-2-222000000000000220000000022-2-20000000000000000
χ25222-2-2-2-2222-2-22-2-2-222-2200000000002i2i−2i−2i00000022-2-22i2i−2i−2i00000000000000000000
χ26222-2-2-2-2222-2-22-2-2-222-2200000000002i2i−2i−2i000000-2-222−2i−2i2i2i00000000000000000000
χ27222-2-2-2-2222-2-22-2-2-222-220000000000−2i−2i2i2i00000022-2-2−2i−2i2i2i00000000000000000000
χ28222-2-2-2-2222-2-22-2-2-222-220000000000−2i−2i2i2i000000-2-2222i2i−2i−2i00000000000000000000
χ292-2-222-2-222-22-22-22-2-222-2002-22-200002i−2i2i−2i0000000000000000000000000000002i−2i00
χ302-2-222-2-222-22-22-22-2-222-2002-22-20000−2i2i−2i2i000000000000000000000000000000−2i2i00
χ312-2-222-2-222-22-22-22-2-222-200-22-2200002i−2i2i−2i000000000000000000000000000000−2i2i00
χ322-2-222-2-222-22-22-22-2-222-200-22-220000−2i2i−2i2i0000000000000000000000000000002i−2i00
χ332-2-222-2-222-22-2-22-222-2-22000000000000002i−2i2i−2i002-22-200000000000000000000002i−2i
χ342-2-222-2-222-22-2-22-222-2-22000000000000002i−2i2i−2i00-22-220000000000000000000000−2i2i
χ352-2-222-2-222-22-2-22-222-2-2200000000000000−2i2i−2i2i002-22-20000000000000000000000−2i2i
χ362-2-222-2-222-22-2-22-222-2-2200000000000000−2i2i−2i2i00-22-2200000000000000000000002i−2i
χ372-2-222-2-22-22-22-222-222-2-2002-2-22000000002i−2i−2i2i000000000000000000002i−2i00000000
χ382-2-222-2-22-22-22-222-222-2-2002-2-2200000000−2i2i2i−2i00000000000000000000−2i2i00000000
χ392-2-222-2-22-22-22-222-222-2-200-222-2000000002i−2i−2i2i00000000000000000000−2i2i00000000
χ402-2-222-2-22-22-22-222-222-2-200-222-200000000−2i2i2i−2i000000000000000000002i−2i00000000
χ412-2-2-2-22222-2-2222-22-22-2-20000002i−2i2i−2i2-2-22000000000000000000000000002i−2i000000
χ422-2-2-2-22222-2-2222-22-22-2-20000002i−2i2i−2i-222-200000000000000000000000000−2i2i000000
χ432-2-2-2-22222-2-2222-22-22-2-2000000−2i2i−2i2i2-2-2200000000000000000000000000−2i2i000000
χ442-2-2-2-22222-2-2222-22-22-2-2000000−2i2i−2i2i-222-2000000000000000000000000002i−2i000000
χ452-2-2-2-22222-2-22-2-22-22-2222-200000000000000002-22-2-220000000000000000002-20000
χ462-2-2-2-22222-2-22-2-22-22-2222-200000000000000002-2-222-2000000000000000000-220000
χ472-2-2-2-22222-2-22-2-22-22-222-220000000000000000-222-2-22000000000000000000-220000
χ482-2-2-2-22222-2-22-2-22-22-222-220000000000000000-22-222-20000000000000000002-20000
χ492-2-2-2-2222-222-2222-2-2-2-222-200002i−2i−2i2i00000000-2200000000000000002i−2i0000000000
χ502-2-2-2-2222-222-2222-2-2-2-222-20000−2i2i2i−2i00000000-220000000000000000−2i2i0000000000
χ512-2-2-2-2222-222-2222-2-2-2-22-2200002i−2i−2i2i000000002-20000000000000000−2i2i0000000000
χ522-2-2-2-2222-222-2222-2-2-2-22-220000−2i2i2i−2i000000002-200000000000000002i−2i0000000000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ54444-4-4-4-4444-4-4-4444-4-44-4000000000000000000000000000000000000000000000000
χ55444-4-4-4-44-4-4444-4444-4-4-4000000000000000000000000000000000000000000000000
χ56444-4-4-4-44-4-444-44-4-4-4444000000000000000000000000000000000000000000000000
χ574-444-44-4-40000000000000000000000000000000000002i−2i2i−2i002i2−2i222−2200000000000000
χ584-444-44-4-40000000000000000000000000000000000002i−2i2i−2i00−2i22i2−222200000000000000
χ594-444-44-4-4000000000000000000000000000000000000−2i2i−2i2i002i2−2i2−222200000000000000
χ604-444-44-4-4000000000000000000000000000000000000−2i2i−2i2i00−2i22i222−2200000000000000
χ614-44-44-44-40000000000000000000000000000000000002-2-222i2−2i200002i2−2i2000000000000
χ624-44-44-44-40000000000000000000000000000000000002-2-22−2i22i20000−2i22i2000000000000
χ634-44-44-44-4000000000000000000000000000000000000-222-22i2−2i20000−2i22i2000000000000
χ644-44-44-44-4000000000000000000000000000000000000-222-2−2i22i200002i2−2i2000000000000
χ654-4-444-4-44-44-444-4-44-4-444000000000000000000000000000000000000000000000000
χ664-4-4-4-4444-444-4-4-4-44444-4000000000000000000000000000000000000000000000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ6888-8-888-8-8000000000000000000000000000000000000000000000000000000000000

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