Finite Group Databasebeta

← Group #420170

Character table — Group #420170

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222888888888888888888888888888888888888161616161616161616161616
order12222222222244444444222244444444444444444444444488888888224488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111
χ5111111111111111111111111-1-1-1-11111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111
χ911111111111111111111-1-1-1-1111111111111-1-11111-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111
χ1011111111111111111111-1-1-1-11111111111-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ1111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111-1-1111111111111-1-1-1-1-1-11111-1-1
χ1211111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-111111111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111111111111111-1-1-1-111-1-1-1-111
χ1722222222-2-2-2-222-2-22-22-2000000000000220022-2-200-2-20000000022-2-2000000000000
χ1822222222-2-2-2-222-2-22-22-20000000000002200-2-2-2-2002200000000-2-222000000000000
χ1922222222-2-2-2-222-2-22-22-2000000000000-2-200222200-2-200000000-2-222000000000000
χ2022222222-2-2-2-222-2-22-22-2000000000000-2-200-2-22200220000000022-2-2000000000000
χ2122222222-2-2-2-2-2-222-22-22000022-2-2000000220000-2-200000022-2-20000000000000000
χ2222222222-2-2-2-2-2-222-22-22000022-2-2000000-2-2000022000000-2-2220000000000000000
χ2322222222-2-2-2-2-2-222-22-220000-2-222000000220000-2-2000000-2-2220000000000000000
χ2422222222-2-2-2-2-2-222-22-220000-2-222000000-2-200002200000022-2-20000000000000000
χ25222-2-22-2-222-2-22-22-2-2-22200002i−2i2i−2i000000002i−2i00002i−2i0000000000002-20000000000
χ26222-2-22-2-222-2-22-22-2-2-22200002i−2i2i−2i00000000−2i2i0000−2i2i000000000000-220000000000
χ27222-2-22-2-222-2-22-22-2-2-2220000−2i2i−2i2i000000002i−2i00002i−2i000000000000-220000000000
χ28222-2-22-2-222-2-22-22-2-2-2220000−2i2i−2i2i00000000−2i2i0000−2i2i0000000000002-20000000000
χ29222-2-22-2-2-2-2222-2-22-222-20000000022-2-200002i−2i0000−2i2i0000000000000000002i−2i0000
χ30222-2-22-2-2-2-2222-2-22-222-20000000022-2-20000−2i2i00002i−2i000000000000000000−2i2i0000
χ31222-2-22-2-2-2-2222-2-22-222-200000000-2-22200002i−2i0000−2i2i000000000000000000−2i2i0000
χ32222-2-22-2-2-2-2222-2-22-222-200000000-2-2220000−2i2i00002i−2i0000000000000000002i−2i0000
χ33222-2-22-2-2-2-222-222-22-2-2222-2-22i−2i−2i2i000000000000000000000000000000002i−2i000000
χ34222-2-22-2-2-2-222-222-22-2-2222-2-2−2i2i2i−2i00000000000000000000000000000000−2i2i000000
χ35222-2-22-2-2-2-222-222-22-2-22-2-2222i−2i−2i2i00000000000000000000000000000000−2i2i000000
χ36222-2-22-2-2-2-222-222-22-2-22-2-222−2i2i2i−2i000000000000000000000000000000002i−2i000000
χ372-2222-2-2-22-22-22-2-2-222-222-22-200002i−2i2i−2i0000000000002i2i−2i−2i00000000000000000000
χ382-2222-2-2-22-22-22-2-2-222-222-22-20000−2i2i−2i2i000000000000−2i−2i2i2i00000000000000000000
χ392-2222-2-2-22-22-22-2-2-222-22-22-2200002i−2i2i−2i000000000000−2i−2i2i2i00000000000000000000
χ402-2222-2-2-22-22-22-2-2-222-22-22-220000−2i2i−2i2i0000000000002i2i−2i−2i00000000000000000000
χ412-22-2-2-2222-2-22-2-22-2222-20000000000002-22-2002-22-200000000000000002-200000000
χ422-22-2-2-2222-2-22-2-22-2222-20000000000002-2-22002-2-220000000000000000-2200000000
χ432-22-2-2-2222-2-22-2-22-2222-2000000000000-222-200-222-20000000000000000-2200000000
χ442-22-2-2-2222-2-22-2-22-2222-2000000000000-22-2200-22-2200000000000000002-200000000
χ452-22-2-2-222-222-2222-2-22-2-2000000002i−2i−2i2i002-20000-220000000000000000000000002i−2i
χ462-22-2-2-222-222-2222-2-22-2-2000000002i−2i−2i2i00-2200002-2000000000000000000000000−2i2i
χ472-22-2-2-222-222-2222-2-22-2-200000000−2i2i2i−2i002-20000-22000000000000000000000000−2i2i
χ482-22-2-2-222-222-2222-2-22-2-200000000−2i2i2i−2i00-2200002-20000000000000000000000002i−2i
χ492-22-2-2-222-222-2-2-2-222-2222-2-22000000002-20000-220000000000000000000000002-200
χ502-22-2-2-222-222-2-2-2-222-2222-2-2200000000-2200002-2000000000000000000000000-2200
χ512-22-2-2-222-222-2-2-2-222-222-222-2000000002-20000-22000000000000000000000000-2200
χ522-22-2-2-222-222-2-2-2-222-222-222-200000000-2200002-20000000000000000000000002-200
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ54444-4-44-4-444-4-4-44-4444-4-4000000000000000000000000000000000000000000000000
χ5544-44-4-44-40000000000000000000000000000000000002i−2i2i−2i22−2200002i2−2i2000000000000
χ5644-44-4-44-40000000000000000000000000000000000002i−2i2i−2i−22220000−2i22i2000000000000
χ5744-44-4-44-4000000000000000000000000000000000000−2i2i−2i2i22−220000−2i22i2000000000000
χ5844-44-4-44-4000000000000000000000000000000000000−2i2i−2i2i−222200002i2−2i2000000000000
χ594-4444-4-4-44-44-4-4444-4-44-4000000000000000000000000000000000000000000000000
χ604-4444-4-4-4-44-444-4444-4-4-4000000000000000000000000000000000000000000000000
χ614-4444-4-4-4-44-44-44-4-4-4444000000000000000000000000000000000000000000000000
χ624-44-4-4-4444-4-4444-44-4-4-44000000000000000000000000000000000000000000000000
χ634-4-44-44-440000000000000000000000000000000000002-2-220022−2222−2200000000000000
χ644-4-44-44-440000000000000000000000000000000000002-2-2200−2222−222200000000000000
χ654-4-44-44-44000000000000000000000000000000000000-222-20022−22−222200000000000000
χ664-4-44-44-44000000000000000000000000000000000000-222-200−222222−2200000000000000
χ6788-8-88-8-88000000000000000000000000000000000000000000000000000000000000
χ688-8-8-8888-8000000000000000000000000000000000000000000000000000000000000

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