Finite Group Databasebeta

← Group #453309

Character table — Group #453309

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222222222888888888888888888888888161616161616161616161616161616161616
order12222222222222222222444444444444444444444444444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ51111111111111111111111-1-111-1-111111111-1-1-1-111111-1-11-1-111-1-111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11111-1-1-1-111-1-111
χ71111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-11111-1-111-1-1
χ81111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-111-1-1111111
χ911111111111111111111-1-111-1-11111111111-1-1-1-11111-11-1-11-1-1-111-1-111-1-1-1-1
χ1011111111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-111-11-1-11111-1-1-1-111
χ1111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11-111-1111-1-1-1-11111-1-1
χ1211111111111111111111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-11-111-1-111-1-11111
χ1311111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-11-1-11-1-1-1-1-1-1-1-11111
χ1411111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-111-1-1-1-1-1111111-1-1
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-111-11111-1-1-1-1-1-111
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1111111111-1-1-1-1
χ1722222222222-2-2-2-2-2-2-2-22000000000000000022-2-222-2-200200-2000000000000
χ1822222222222-2-2-2-2-2-2-2-22000000000000000022-2-2-2-22200-2002000000000000
χ1922222222222-2-2-2-2-2-2-2-220000000000000000-2-22222-2-200-2002000000000000
χ2022222222222-2-2-2-2-2-2-2-220000000000000000-2-222-2-22200200-2000000000000
χ2122222222-2-2-222-2-222-2-2-2002200-2-20000000000002-22-20200-20000000000000
χ2222222222-2-2-222-2-222-2-2-2002200-2-2000000000000-22-220-20020000000000000
χ2322222222-2-2-222-2-222-2-2-200-2-200220000000000002-22-20-20020000000000000
χ2422222222-2-2-222-2-222-2-2-200-2-20022000000000000-22-220200-20000000000000
χ2522222222-2-2-2-2-222-2-222-22200-2-2000000000000002-2-22-200200000000000000
χ2622222222-2-2-2-2-222-2-222-22200-2-200000000000000-222-2200-200000000000000
χ2722222222-2-2-2-2-222-2-222-2-2-20022000000000000002-2-22200-200000000000000
χ2822222222-2-2-2-2-222-2-222-2-2-2002200000000000000-222-2-200200000000000000
χ29222-22-2-2-222-2222-2-2-22-2-22-2002-200000022-2-20000000000000000002-2000000
χ30222-22-2-2-222-2222-2-2-22-2-22-2002-2000000-2-222000000000000000000-22000000
χ31222-22-2-2-222-2222-2-2-22-2-2-2200-2200000022-2-2000000000000000000-22000000
χ32222-22-2-2-222-2222-2-2-22-2-2-2200-22000000-2-2220000000000000000002-2000000
χ33222-22-2-2-2-2-22-2-22-2222-222-200-22002i2i−2i−2i0000000000000000002i−2i0000000000
χ34222-22-2-2-2-2-22-2-22-2222-222-200-2200−2i−2i2i2i000000000000000000−2i2i0000000000
χ35222-22-2-2-2-2-22-2-22-2222-22-22002-2002i2i−2i−2i000000000000000000−2i2i0000000000
χ36222-22-2-2-2-2-22-2-22-2222-22-22002-200−2i−2i2i2i0000000000000000002i−2i0000000000
χ3722-22-22-2-22-222-2222-2-2-2-2002-2002-22-22-2000000000000000000002-200000000
χ3822-22-22-2-22-222-2222-2-2-2-2002-2002-2-22-2200000000000000000000-2200000000
χ3922-22-22-2-22-222-2222-2-2-2-200-2200-222-22-200000000000000000000-2200000000
χ4022-22-22-2-22-222-2222-2-2-2-200-2200-22-22-22000000000000000000002-200000000
χ4122-22-22-2-2-22-22-2-2-22-2222002-200-2200002i−2i2i−2i000000000000000000002i−2i0000
χ4222-22-22-2-2-22-22-2-2-22-2222002-200-220000−2i2i−2i2i00000000000000000000−2i2i0000
χ4322-22-22-2-2-22-22-2-2-22-222200-22002-200002i−2i2i−2i00000000000000000000−2i2i0000
χ4422-22-22-2-2-22-22-2-2-22-222200-22002-20000−2i2i−2i2i000000000000000000002i−2i0000
χ4522-2-2-2-222-2222-2-22-222-2-20000000000002i−2i−2i2i2-22-2000000000000000000002i−2i
χ4622-2-2-2-222-2222-2-22-222-2-20000000000002i−2i−2i2i-22-2200000000000000000000−2i2i
χ4722-2-2-2-222-2222-2-22-222-2-2000000000000−2i2i2i−2i2-22-200000000000000000000−2i2i
χ4822-2-2-2-222-2222-2-22-222-2-2000000000000−2i2i2i−2i-22-22000000000000000000002i−2i
χ4922-2-2-2-222-222-222-22-2-22-2000000002i−2i−2i2i00002-2-220000000000000000002i−2i00
χ5022-2-2-2-222-222-222-22-2-22-2000000002i−2i−2i2i0000-222-2000000000000000000−2i2i00
χ5122-2-2-2-222-222-222-22-2-22-200000000−2i2i2i−2i00002-2-22000000000000000000−2i2i00
χ5222-2-2-2-222-222-222-22-2-22-200000000−2i2i2i−2i0000-222-20000000000000000002i−2i00
χ53444-44-4-4-444-4-4-4-4444-44-4000000000000000000000000000000000000000000
χ54444-44-4-4-4-4-4444-44-4-4-444000000000000000000000000000000000000000000
χ5544-44-44-4-44-44-44-4-4-4444-4000000000000000000000000000000000000000000
χ5644-44-44-4-4-44-4-4444-44-4-44000000000000000000000000000000000000000000
χ5744-4-4-4-4444-4-44-44-4-44-444000000000000000000000000000000000000000000
χ5844-4-4-4-4444-4-4-44-444-44-44000000000000000000000000000000000000000000
χ598-888-8-88-8000000000000000000000000000000000000000000000000000000
χ608-88-8-88-88000000000000000000000000000000000000000000000000000000
χ618-8-888-8-88000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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