Finite Group Databasebeta

← Group #346616

Character table — Group #346616

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77
size111111112222222222224444444444444444444444888888888888888888888888816161616161616163232
order12222222222244444444222222222222222244444422222222444444444888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1111111111111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-1111111111111-1-1-1-11111-1-1
χ611111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1
χ911111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-11-1
χ1011111111-1-1-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-111-1-111-11
χ1111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-111-1-1-1-1111111-1-1-1-111-1-1-1-111-11
χ1211111111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-111-1-1-1-111-1-1-1-11111-1-11111-1-11-1
χ1311111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-11
χ1411111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-11111-1-1-1-1-1-1111111-1-1-1-1111-1
χ1511111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1111-1
χ1611111111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-111-1-111-1-1-1-1111111-1-111-1-1-11
χ1722222222222222-2-222-2-2000000002222222222-2-2-2-200000000-20000-2-2-2-2000000000000000000
χ1822222222222222-2-222-2-200000000-2-2-2-2-2-2-2-222-2-2-2-200000000-200002222000000000000000000
χ19222222222222-2-222-2-2222222222200000000-2-222-2-200000000-2-2-2-2-20000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-2-2-2-200000000-2-222-2-200000000-222220000000000000000000000
χ21222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-22222-2-222-2-2200000000000000000000000000
χ22222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-222-2-222-2-222200000000000000000000000000
χ2322222222-2-2-2-222-2-222-2-2000000002222-2-2-2-2-2-222-2-20000000020000-2-222000000000000000000
χ2422222222-2-2-2-222-2-222-2-200000000-2-2-2-22222-2-222-2-2000000002000022-2-2000000000000000000
χ2522222222-2-2-2-2-2-222-2-2222222-2-2-2-20000000022-2-2-2-2000000002-2-2220000000000000000000000
χ2622222222-2-2-2-2-2-222-2-222-2-2-2-222220000000022-2-2-2-200000000222-2-20000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2000000000000000022222222-2-2-2-222-200000000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000222222-2-22222-2-2-200000000000000000000000000
χ29222-2-2-22-222-2-22200-2-2000000000022-2-222-2-22-2000000000000000000000i2i2−i2−i2i2i2−i2−i20000i2−i2i2−i200
χ30222-2-2-22-222-2-22200-2-2000000000022-2-222-2-22-2000000000000000000000−i2−i2i2i2−i2−i2i2i20000−i2i2−i2i200
χ31222-2-2-22-222-2-22200-2-20000000000-2-222-2-2222-2000000000000000000000i2i2−i2−i2i2i2−i2−i20000−i2i2−i2i200
χ32222-2-2-22-222-2-22200-2-20000000000-2-222-2-2222-2000000000000000000000−i2−i2i2i2−i2−i2i2i20000i2−i2i2−i200
χ33222-2-2-22-2-2-2222200-2-2000000000022-2-2-2-222-22000000000000000000000i2i2−i2−i2−i2−i2i2i20000i2−i2−i2i200
χ34222-2-2-22-2-2-2222200-2-2000000000022-2-2-2-222-22000000000000000000000−i2−i2i2i2i2i2−i2−i20000−i2i2i2−i200
χ35222-2-2-22-2-2-2222200-2-20000000000-2-22222-2-2-22000000000000000000000i2i2−i2−i2−i2−i2i2i20000−i2i2i2−i200
χ36222-2-2-22-2-2-2222200-2-20000000000-2-22222-2-2-22000000000000000000000−i2−i2i2i2i2i2−i2−i20000i2−i2−i2i200
χ3722-2-2-22-222-22-200-2-2002222-2-222-2-200000000002-200000000000000000002−22−22−22−22−22−2000000
χ3822-2-2-22-222-22-200-2-2002222-2-222-2-200000000002-20000000000000000000−22−22−22−22−22−22000000
χ3922-2-2-22-222-22-200-2-20022-2-222-2-22200000000002-200000000000000000002−22−22−22−2−22−22000000
χ4022-2-2-22-222-22-200-2-20022-2-222-2-22200000000002-20000000000000000000−22−22−22−222−22−2000000
χ4122-2-2-22-22-22-2200-2-2002222-2-2-2-2220000000000-2200000000000000000002−22−2−22−222−2−22000000
χ4222-2-2-22-22-22-2200-2-2002222-2-2-2-2220000000000-220000000000000000000−22−222−22−2−222−2000000
χ4322-2-2-22-22-22-2200-2-20022-2-22222-2-20000000000-2200000000000000000002−22−2−22−22−222−2000000
χ4422-2-2-22-22-22-2200-2-20022-2-22222-2-20000000000-220000000000000000000−22−222−22−22−2−22000000
χ452-2-2-22-22200002-22-22-22-200002-22-200002-22-200002-22-22-200000002-2002-2000000000000000000
χ462-2-2-22-22200002-22-22-22-200002-22-20000-22-2200002-2-22-2200000002-200-22000000000000000000
χ472-2-2-22-22200002-22-22-22-20000-22-2200002-22-200002-2-22-220000000-22002-2000000000000000000
χ482-2-2-22-22200002-22-22-22-20000-22-220000-22-2200002-22-22-20000000-2200-22000000000000000000
χ492-2-2-22-22200002-2-222-2-222-22-2000000002-22-20000-2200002-22-202-20000-22000000000000000000
χ502-2-2-22-22200002-2-222-2-222-22-200000000-22-220000-220000-22-2202-200002-2000000000000000000
χ512-2-2-22-22200002-2-222-2-22-22-22000000002-22-20000-220000-22-220-220000-22000000000000000000
χ522-2-2-22-22200002-2-222-2-22-22-2200000000-22-220000-2200002-22-20-2200002-2000000000000000000
χ532-2-2-22-2220000-222-2-222-200002-22-22-22-200000000-2200002-2-22000-222-200000000000000000000
χ542-2-2-22-2220000-222-2-222-200002-22-2-22-2200000000-220000-222-2000-22-2200000000000000000000
χ552-2-2-22-2220000-222-2-222-20000-22-222-22-200000000-220000-222-20002-22-200000000000000000000
χ562-2-2-22-2220000-222-2-222-20000-22-22-22-2200000000-2200002-2-220002-2-2200000000000000000000
χ572-2-2-22-2220000-22-22-22-222-22-200002-22-2000000002-22-2-2200000-2200-2200000000000000000000
χ582-2-2-22-2220000-22-22-22-222-22-20000-22-22000000002-2-222-200000-22002-200000000000000000000
χ592-2-2-22-2220000-22-22-22-22-22-2200002-22-2000000002-2-222-2000002-200-2200000000000000000000
χ602-2-2-22-2220000-22-22-22-22-22-220000-22-22000000002-22-2-22000002-2002-200000000000000000000
χ61444-4-4-44-444-4-4-4-40044000000000000000000-44000000000000000000000000000000000000000
χ62444-4-4-44-4-4-444-4-400440000000000000000004-4000000000000000000000000000000000000000
χ6344-444-4-4-44-4-44000000000000000000000000000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000
χ6444-444-4-4-44-4-4400000000000000000000000000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000
χ6544-444-4-4-4-444-4000000000000000000000000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000
χ6644-444-4-4-4-444-400000000000000000000000000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000
χ6744-4-4-44-444-44-4004400-4-4000000000000000000-440000000000000000000000000000000000000
χ6844-4-4-44-44-44-44004400-4-40000000000000000004-40000000000000000000000000000000000000
χ694-444-4-4-440000004-400-444-4-4400000000000000000000000000000000000000000000000000000
χ704-444-4-4-440000004-400-44-444-400000000000000000000000000000000000000000000000000000
χ714-444-4-4-44000000-44004-400004-4-440000000000000000000000000000000000000000000000000
χ724-444-4-4-44000000-44004-40000-444-40000000000000000000000000000000000000000000000000
χ734-4-44-444-400004-400-44000000000000004-4-4400000000000000000000000000000000000000000
χ744-4-44-444-400004-400-4400000000000000-444-400000000000000000000000000000000000000000
χ754-4-44-444-40000-44004-400000000004-4-44000000000000000000000000000000000000000000000
χ764-4-44-444-40000-44004-40000000000-444-4000000000000000000000000000000000000000000000
χ778-88-888-8-8000000000000000000000000000000000000000000000000000000000000000000000

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