Finite Group Databasebeta

← Group #449597

Character table — Group #449597

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222888888888888888888888888888888888888161616161616161616161616
order12222222222244444444222222444444444444444444444488888888444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1
χ61111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111
χ71111111111111111111111-1-1-1-11111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1111111-1-1
χ911111111111111111111-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ1011111111111111111111-1-11111-1-1-1-11111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ1111111111111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1
χ1211111111111111111111-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111
χ1311111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ1411111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111
χ1511111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1111111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ1722222222-2-2-2-22-2222-2-2-200002222-2-200000000-2-200000000000022-2-2000000000000
χ1822222222-2-2-2-22-2222-2-2-2000022-2-22200000000-2-2000000000000-2-222000000000000
χ1922222222-2-2-2-22-2222-2-2-20000-2-222-2-20000000022000000000000-2-222000000000000
χ2022222222-2-2-2-22-2222-2-2-20000-2-2-2-222000000002200000000000022-2-2000000000000
χ2122222222-2-2-2-2-22-2-2-222222220000000000-2-2-2-2000000000022-2-20000000000000000
χ2222222222-2-2-2-2-22-2-2-222222-2-20000000000-2-2220000000000-2-2220000000000000000
χ2322222222-2-2-2-2-22-2-2-2222-2-222000000000022-2-20000000000-2-2220000000000000000
χ2422222222-2-2-2-2-22-2-2-2222-2-2-2-200000000002222000000000022-2-20000000000000000
χ25222-2-2-2-2222-2-22-22-2-222-20000002i−2i2i−2i000000000022-2-200000000000000000000002i−2i
χ26222-2-2-2-2222-2-22-22-2-222-20000002i−2i2i−2i0000000000-2-2220000000000000000000000−2i2i
χ27222-2-2-2-2222-2-22-22-2-222-2000000−2i2i−2i2i000000000022-2-20000000000000000000000−2i2i
χ28222-2-2-2-2222-2-22-22-2-222-2000000−2i2i−2i2i0000000000-2-22200000000000000000000002i−2i
χ29222-2-2-2-2222-2-2-22-222-2-22002-20000002i2i−2i−2i002-20000000000000000000000002i−2i0000
χ30222-2-2-2-2222-2-2-22-222-2-22002-2000000−2i−2i2i2i002-2000000000000000000000000−2i2i0000
χ31222-2-2-2-2222-2-2-22-222-2-2200-220000002i2i−2i−2i00-22000000000000000000000000−2i2i0000
χ32222-2-2-2-2222-2-2-22-222-2-2200-22000000−2i−2i2i2i00-220000000000000000000000002i−2i0000
χ33222-2-2-2-22-2-222222-2-2-2-22002-2002i−2i−2i2i000000-220000000000000000002i−2i0000000000
χ34222-2-2-2-22-2-222222-2-2-2-22002-200−2i2i2i−2i000000-22000000000000000000−2i2i0000000000
χ35222-2-2-2-22-2-222222-2-2-2-2200-22002i−2i−2i2i0000002-2000000000000000000−2i2i0000000000
χ36222-2-2-2-22-2-222222-2-2-2-2200-2200−2i2i2i−2i0000002-20000000000000000002i−2i0000000000
χ372-2-22-22-222-22-222-22-22-2-200000000002i−2i2i−2i0000002-22-22i2i−2i−2i00000000000000000000
χ382-2-22-22-222-22-222-22-22-2-200000000002i−2i2i−2i000000-22-22−2i−2i2i2i00000000000000000000
χ392-2-22-22-222-22-222-22-22-2-20000000000−2i2i−2i2i0000002-22-2−2i−2i2i2i00000000000000000000
χ402-2-22-22-222-22-222-22-22-2-20000000000−2i2i−2i2i000000-22-222i2i−2i−2i00000000000000000000
χ412-2-2-22-2222-2-222-2-2-222-222-20000000000002-200002-2-2200000000000000002-2000000
χ422-2-2-22-2222-2-222-2-2-222-222-20000000000002-20000-222-20000000000000000-22000000
χ432-2-2-22-2222-2-222-2-2-222-22-22000000000000-2200002-2-220000000000000000-22000000
χ442-2-2-22-2222-2-222-2-2-222-22-22000000000000-220000-222-200000000000000002-2000000
χ452-2-2-22-2222-2-22-2222-2-22-200002-200002-2-2200002-20000000000000000000000002-200
χ462-2-2-22-2222-2-22-2222-2-22-200002-20000-222-200002-2000000000000000000000000-2200
χ472-2-2-22-2222-2-22-2222-2-22-20000-2200002-2-220000-22000000000000000000000000-2200
χ482-2-2-22-2222-2-22-2222-2-22-20000-220000-222-20000-220000000000000000000000002-200
χ492-2-2-22-222-222-2-2-222-22-222-2002-200000000-2200-220000000000000000002-200000000
χ502-2-2-22-222-222-2-2-222-22-222-200-2200000000-22002-2000000000000000000-2200000000
χ512-2-2-22-222-222-2-2-222-22-22-22002-2000000002-200-22000000000000000000-2200000000
χ522-2-2-22-222-222-2-2-222-22-22-2200-22000000002-2002-20000000000000000002-200000000
χ53444444444444-4-4-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ54444-4-4-4-44-4-444-4-4-44444-4000000000000000000000000000000000000000000000000
χ5544-444-4-4-40000000000000000000000000000000000002-22-222−220022−2200000000000000
χ5644-444-4-4-40000000000000000000000000000000000002-22-2−222200−222200000000000000
χ5744-444-4-4-4000000000000000000000000000000000000-22-2222−2200−222200000000000000
χ5844-444-4-4-4000000000000000000000000000000000000-22-22−22220022−2200000000000000
χ594-444-4-44-40000000000000000000000000000000000002i−2i−2i2i002i2−2i20022−22000000000000
χ604-444-4-44-40000000000000000000000000000000000002i−2i−2i2i00−2i22i200−2222000000000000
χ614-444-4-44-4000000000000000000000000000000000000−2i2i2i−2i002i2−2i200−2222000000000000
χ624-444-4-44-4000000000000000000000000000000000000−2i2i2i−2i00−2i22i20022−22000000000000
χ634-4-44-44-444-44-4-4-44-44-444000000000000000000000000000000000000000000000000
χ644-4-44-44-44-44-444-4-44-4-444000000000000000000000000000000000000000000000000
χ654-4-44-44-44-44-44-444-444-4-4000000000000000000000000000000000000000000000000
χ664-4-4-44-444-444-444-4-44-44-4000000000000000000000000000000000000000000000000
χ6788-8-8-888-8000000000000000000000000000000000000000000000000000000000000
χ688-88-888-8-8000000000000000000000000000000000000000000000000000000000000

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