Finite Group Databasebeta

← Group #501405

Character table — Group #501405

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11222222244444444444444448888888888888888888888161616161616161632323232
order122224444222244448888888824888816161616161616161616161616161616444488882488
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111-1-111-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11-11-1
χ611111111111-1-111-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-11-11
χ711111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-11-11
χ811111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ9111111111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ10111111111-1-111-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ11111111111-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111
χ12111111111-1-111-1-11111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1
χ13111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-1111-1-11
χ14111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-111-1
χ15111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-111-1-1-1-111-111-1
χ16111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1-1-1-111111111-1-1-1-1-1-11111-1-11-1-11
χ1722222222222222222-2-2-2-2-2-2-2-222-2-2-2-20000000000000000000000000000
χ1822222222222-2-222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000000000000000
χ19222222222-2-222-2-222-2-22222-2-2-2-2-2-2220000000000000000000000000000
χ20222222222-2-2-2-2-2-2-2-2-2-22222-2-22222-2-20000000000000000000000000000
χ2122222-2-2-2-2002200-2-2002i2i−2i−2i0000002i−2i22−2−2i2i2−i2−i222−2−2i2i2−i2−i2000000000000
χ2222222-2-2-2-2002200-2-2002i2i−2i−2i0000002i−2i−2−222−i2−i2i2i2−2−222−i2−i2i2i2000000000000
χ2322222-2-2-2-2002200-2-200−2i−2i2i2i000000−2i2i22−2−2−i2−i2i2i222−2−2−i2−i2i2i2000000000000
χ2422222-2-2-2-2002200-2-200−2i−2i2i2i000000−2i2i−2−222i2i2−i2−i2−2−222i2i2−i2−i2000000000000
χ2522222-2-2-2-200-2-20022002i2i−2i−2i000000−2i2i22−2−2i2i2−i2−i2−2−222−i2−i2i2i2000000000000
χ2622222-2-2-2-200-2-20022002i2i−2i−2i000000−2i2i−2−222−i2−i2i2i222−2−2i2i2−i2−i2000000000000
χ2722222-2-2-2-200-2-2002200−2i−2i2i2i0000002i−2i22−2−2−i2−i2i2i2−2−222i2i2−i2−i2000000000000
χ2822222-2-2-2-200-2-2002200−2i−2i2i2i0000002i−2i−2−222i2i2−i2−i222−2−2−i2−i2i2i2000000000000
χ29222-2-22-22-22-2002-2002-22-22-22-20000000000000000000000002i−2i002i−2i0000
χ30222-2-22-22-22-2002-2002-22-22-22-2000000000000000000000000−2i2i00−2i2i0000
χ31222-2-22-22-22-2002-200-22-22-22-2200000000000000000000002i−2i002i−2i000000
χ32222-2-22-22-22-2002-200-22-22-22-220000000000000000000000−2i2i00−2i2i000000
χ33222-2-22-22-2-2200-22002-2-22-222-20000000000000000000000002i−2i00−2i2i0000
χ34222-2-22-22-2-2200-22002-2-22-222-2000000000000000000000000−2i2i002i−2i0000
χ35222-2-22-22-2-2200-2200-222-22-2-2200000000000000000000002i−2i00−2i2i000000
χ36222-2-22-22-2-2200-2200-222-22-2-220000000000000000000000−2i2i002i−2i000000
χ3722-22-222-2-2222-2-2-22-2000000002-20000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000
χ3822-22-222-2-2222-2-2-22-2000000002-20000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000
χ3922-22-222-2-222-22-2-2-2200000000-220000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000
χ4022-22-222-2-222-22-2-2-2200000000-220000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000
χ4122-22-222-2-2-2-22-2222-200000000-220000i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4222-22-222-2-2-2-22-2222-200000000-220000−i2i2−i2i2i2−i2i2−i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4322-22-222-2-2-2-2-2222-22000000002-20000i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ4422-22-222-2-2-2-2-2222-22000000002-20000−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ4522-22-2-2-222002-200-22220000-2-2002-2002i−2i−2i2i00002i−2i−2i2i0000000000000000
χ4622-22-2-2-222002-200-22220000-2-2002-200−2i2i2i−2i0000−2i2i2i−2i0000000000000000
χ4722-22-2-2-222002-200-22-2-200002200-220000002-2-2200002-2-22000000000000
χ4822-22-2-2-222002-200-22-2-200002200-22000000-222-20000-222-2000000000000
χ4922-22-2-2-22200-22002-2220000-2-200-22002i−2i−2i2i0000−2i2i2i−2i0000000000000000
χ5022-22-2-2-22200-22002-2220000-2-200-2200−2i2i2i−2i00002i−2i−2i2i0000000000000000
χ5122-22-2-2-22200-22002-2-2-2000022002-20000002-2-220000-222-2000000000000
χ5222-22-2-2-22200-22002-2-2-2000022002-2000000-222-200002-2-22000000000000
χ53444-4-4-44-4400000000004i−4i−4i4i000000000000000000000000000000000000
χ54444-4-4-44-440000000000−4i4i4i−4i000000000000000000000000000000000000
χ5544-4-444-4-444-400-4400000000000000000000000000000000000000000000
χ5644-4-444-4-44-44004-400000000000000000000000000000000000000000000
χ5744-4-44-444-4000000004-40000-440000000000000000000000000000000000
χ5844-4-44-444-400000000-4400004-40000000000000000000000000000000000
χ5916-16000000000000000000000000000000000000000000000000000000000

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