Finite Group Databasebeta

← Group #423180

Character table — Group #423180

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11222222222222222888888888888888888888888161616161616161616161616161616161616
order12222222244444444222244448888888888888888224444444488888888
χ111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1
χ31111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-111
χ51111111111111111111-1-111-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111
χ61111111111111111111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1111111-1-1-1-1-1-1
χ71111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-111-1-1
χ81111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111-1-11111
χ911111111111111111-1-111-1-1111111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-111
χ1011111111111111111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1
χ1111111111111111111-1-111-1-111-1-1-1-1111111111111-1-1-1-111-1-111-1-1-1-111-1-1
χ1211111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-11111
χ1311111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ1411111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-11111-1-1
χ1511111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-11111-1-11111-1-1-1-1
χ1611111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-111-1-111
χ17222222222-2-2-2-2-2-2-2-20000000000002i2i−2i−2i00002i2i−2i−2i000000002-200000000
χ18222222222-2-2-2-2-2-2-2-20000000000002i2i−2i−2i0000−2i−2i2i2i00000000-2200000000
χ19222222222-2-2-2-2-2-2-2-2000000000000−2i−2i2i2i00002i2i−2i−2i00000000-2200000000
χ20222222222-2-2-2-2-2-2-2-2000000000000−2i−2i2i2i0000−2i−2i2i2i000000002-200000000
χ212222-22-2-2-2222-2-2-2-222200-2-200000000002i2i−2i−2i0000002i−2i00000000000000
χ222222-22-2-2-2222-2-2-2-222200-2-20000000000−2i−2i2i2i000000−2i2i00000000000000
χ232222-22-2-2-2222-2-2-2-22-2-2002200000000002i2i−2i−2i000000−2i2i00000000000000
χ242222-22-2-2-2222-2-2-2-22-2-200220000000000−2i−2i2i2i0000002i−2i00000000000000
χ25222-22-22-2-222-2-222-2-20000000022-2-200002i−2i2i−2i000000000000000000002i−2i
χ26222-22-22-2-222-2-222-2-20000000022-2-20000−2i2i−2i2i00000000000000000000−2i2i
χ27222-22-22-2-222-2-222-2-200000000-2-22200002i−2i2i−2i00000000000000000000−2i2i
χ28222-22-22-2-222-2-222-2-200000000-2-2220000−2i2i−2i2i000000000000000000002i−2i
χ29222-2-2-2-22222-22-2-22-20000000000002i−2i2i−2i2-2-22000000002i−2i000000000000
χ30222-2-2-2-22222-22-2-22-20000000000002i−2i2i−2i-222-200000000−2i2i000000000000
χ31222-2-2-2-22222-22-2-22-2000000000000−2i2i−2i2i2-2-2200000000−2i2i000000000000
χ32222-2-2-2-22222-22-2-22-2000000000000−2i2i−2i2i-222-2000000002i−2i000000000000
χ33222-2-2-2-222-2-22-222-22002200-2-200002-2-2200000000000000000000002-200
χ34222-2-2-2-222-2-22-222-22002200-2-20000-222-20000000000000000000000-2200
χ35222-2-2-2-222-2-22-222-2200-2-2002200002-2-220000000000000000000000-2200
χ36222-2-2-2-222-2-22-222-2200-2-200220000-222-200000000000000000000002-200
χ3722-222-2-22-22-2-2-2-2222002-2002-22-22-20000000000002-20000000000000000
χ3822-222-2-22-22-2-2-2-2222002-2002-2-22-22000000000000-220000000000000000
χ3922-222-2-22-22-2-2-2-222200-2200-222-22-2000000000000-220000000000000000
χ4022-222-2-22-22-2-2-2-222200-2200-22-22-220000000000002-20000000000000000
χ4122-2-222-2-222-222-22-2-2000000002-2-22000000002i−2i2i−2i0000002i−2i0000000000
χ4222-2-222-2-222-222-22-2-2000000002-2-2200000000−2i2i−2i2i000000−2i2i0000000000
χ4322-2-222-2-222-222-22-2-200000000-222-2000000002i−2i2i−2i000000−2i2i0000000000
χ4422-2-222-2-222-222-22-2-200000000-222-200000000−2i2i−2i2i0000002i−2i0000000000
χ4522-2-222-2-22-22-2-22-2222-2002-2000000000000002-2-2200000000002-2000000
χ4622-2-222-2-22-22-2-22-2222-2002-200000000000000-222-20000000000-22000000
χ4722-2-222-2-22-22-2-22-222-2200-22000000000000002-2-220000000000-22000000
χ4822-2-222-2-22-22-2-22-222-2200-2200000000000000-222-200000000002-2000000
χ4922-2-2-2222-2-22-22-22-222-22-2-22-2200000000000000000000000000002-20000
χ5022-2-2-2222-2-22-22-22-222-2-22-222-20000000000000000000000000000-220000
χ5122-2-2-2222-2-22-22-22-22-222-22-2-220000000000000000000000000000-220000
χ5222-2-2-2222-2-22-22-22-22-22-222-22-200000000000000000000000000002-20000
χ534444-44-4-4-4-4-4-44444-4000000000000000000000000000000000000000000
χ54444-44-44-4-4-4-444-4-444000000000000000000000000000000000000000000
χ5544-444-4-44-4-44444-4-4-4000000000000000000000000000000000000000000
χ5644-44-4-44-444-4-444-4-44000000000000000000000000000000000000000000
χ5744-44-4-44-44-444-4-444-4000000000000000000000000000000000000000000
χ5844-4-4-4444-44-44-44-44-4000000000000000000000000000000000000000000
χ5916-16000000000000000000000000000000000000000000000000000000000

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