Finite Group Databasebeta

← Group #425018

Character table — Group #425018

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222888888888888888888888888888888888888161616161616161616161616
order12222222222244444444222222444444444444444444444488888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ311111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ5111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111
χ6111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111
χ7111111111111111111111111-1-1-1-1-1-111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ911111111111111111111-1-1-1-11111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1
χ1011111111111111111111-1-1-1-1111111-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1
χ1111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ1211111111111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ1311111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1411111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-11111
χ1722222222-2-2-2-222-22-2-2-220000002200000022-2-2-2-200000000000022-2-2000000000000
χ1822222222-2-2-2-222-22-2-2-2200000022000000-2-222-2-2000000000000-2-222000000000000
χ1922222222-2-2-2-222-22-2-2-22000000-2-200000022-2-222000000000000-2-222000000000000
χ2022222222-2-2-2-222-22-2-2-22000000-2-2000000-2-2222200000000000022-2-2000000000000
χ2122222222-2-2-2-2-2-22-2222-200002200-2-222-2-20000000000000022-2-20000000000000000
χ2222222222-2-2-2-2-2-22-2222-200002200-2-2-2-22200000000000000-2-2220000000000000000
χ2322222222-2-2-2-2-2-22-2222-20000-2-2002222-2-200000000000000-2-2220000000000000000
χ2422222222-2-2-2-2-2-22-2222-20000-2-20022-2-2220000000000000022-2-20000000000000000
χ25222-22-2-2-222-2-2222-22-2-2-222-2-22-2002-20000000000000000000000000000002-2000000
χ26222-22-2-2-222-2-2222-22-2-2-222-2-2-2200-22000000000000000000000000000000-22000000
χ27222-22-2-2-222-2-2222-22-2-2-2-2-2222-2002-2000000000000000000000000000000-22000000
χ28222-22-2-2-222-2-2222-22-2-2-2-2-222-2200-220000000000000000000000000000002-2000000
χ29222-22-2-2-222-2-2-2-2-22-2222000000000000002i−2i2i−2i002i2i−2i−2i000000000000000000002-200
χ30222-22-2-2-222-2-2-2-2-22-2222000000000000002i−2i2i−2i00−2i−2i2i2i00000000000000000000-2200
χ31222-22-2-2-222-2-2-2-2-22-222200000000000000−2i2i−2i2i002i2i−2i−2i00000000000000000000-2200
χ32222-22-2-2-222-2-2-2-2-22-222200000000000000−2i2i−2i2i00−2i−2i2i2i000000000000000000002-200
χ33222-22-2-2-2-2-222-2-2222-2-2200002-200-2200002i−2i−2i2i0000000000000000002i−2i0000000000
χ34222-22-2-2-2-2-222-2-2222-2-2200002-200-220000−2i2i2i−2i000000000000000000−2i2i0000000000
χ35222-22-2-2-2-2-222-2-2222-2-220000-22002-200002i−2i−2i2i000000000000000000−2i2i0000000000
χ36222-22-2-2-2-2-222-2-2222-2-220000-22002-20000−2i2i2i−2i0000000000000000002i−2i0000000000
χ372-2-222-2-222-2-222-2-2-222-222-22-200000000000000002-22-222-2-200000000000000000000
χ382-2-222-2-222-2-222-2-2-222-222-22-20000000000000000-22-22-2-22200000000000000000000
χ392-2-222-2-222-2-222-2-2-222-22-22-2200000000000000002-22-2-2-22200000000000000000000
χ402-2-222-2-222-2-222-2-2-222-22-22-220000000000000000-22-2222-2-200000000000000000000
χ412-2-2-2222-22-22-22-2-222-22-22-2-22002i−2i00000000002i−2i000000000000000000000000002i−2i
χ422-2-2-2222-22-22-22-2-222-22-22-2-2200−2i2i0000000000−2i2i00000000000000000000000000−2i2i
χ432-2-2-2222-22-22-22-2-222-22-2-222-2002i−2i00000000002i−2i00000000000000000000000000−2i2i
χ442-2-2-2222-22-22-22-2-222-22-2-222-200−2i2i0000000000−2i2i000000000000000000000000002i−2i
χ452-2-2-2222-22-22-2-222-2-22-2200000000002-22-20000002i−2i−2i2i0000000000000000002i−2i0000
χ462-2-2-2222-22-22-2-222-2-22-2200000000002-22-2000000−2i2i2i−2i000000000000000000−2i2i0000
χ472-2-2-2222-22-22-2-222-2-22-220000000000-22-220000002i−2i−2i2i000000000000000000−2i2i0000
χ482-2-2-2222-22-22-2-222-2-22-220000000000-22-22000000−2i2i2i−2i0000000000000000002i−2i0000
χ492-2-2-2222-2-22-222-222-22-2-20000002i−2i002-2-220000−2i2i0000000000000000002i−2i00000000
χ502-2-2-2222-2-22-222-222-22-2-20000002i−2i00-222-20000−2i2i000000000000000000−2i2i00000000
χ512-2-2-2222-2-22-222-222-22-2-2000000−2i2i002-2-2200002i−2i000000000000000000−2i2i00000000
χ522-2-2-2222-2-22-222-222-22-2-2000000−2i2i00-222-200002i−2i0000000000000000002i−2i00000000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ54444-44-4-4-4-4-44444-4-4-444-4000000000000000000000000000000000000000000000000
χ5544-4-4-44-440000000000000000000000000000000000002-22-222−22000022−22000000000000
χ5644-4-4-44-440000000000000000000000000000000000002-22-2−22220000−2222000000000000
χ5744-4-4-44-44000000000000000000000000000000000000-22-2222−220000−2222000000000000
χ5844-4-4-44-44000000000000000000000000000000000000-22-22−2222000022−22000000000000
χ594-44-4-4-4440000000000000000000000000000000000002-2-220022−2222−2200000000000000
χ604-44-4-4-4440000000000000000000000000000000000002-2-2200−2222−222200000000000000
χ614-44-4-4-444000000000000000000000000000000000000-222-20022−22−222200000000000000
χ624-44-4-4-444000000000000000000000000000000000000-222-200−222222−2200000000000000
χ634-4-444-4-444-4-44-4444-4-44-4000000000000000000000000000000000000000000000000
χ644-4-444-4-44-444-44-44-4-4-444000000000000000000000000000000000000000000000000
χ654-4-444-4-44-444-4-44-4444-4-4000000000000000000000000000000000000000000000000
χ664-4-4-4444-4-44-44-44-4-44-444000000000000000000000000000000000000000000000000
χ6788-88-8-88-8000000000000000000000000000000000000000000000000000000000000
χ688-888-88-8-8000000000000000000000000000000000000000000000000000000000000

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