Finite Group Databasebeta

← Group #270970

Character table — Group #270970

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size11111111222222222222222244444444444444444444444444888888888888888888161616161616161616163232
order12222222222244444444444444444444448888888888888888444444444488888888224444888844
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-1111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1
χ6111111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1
χ911111111-1-1-1-1111-1-1-1-1111111-1-11111-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-1-1-11-11111-1-11-1
χ1011111111-1-1-1-1111-1-1-1-1111111-1-11111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-11-1-1-1-111-11
χ1111111111-1-1-1-1111-1-1-1-1111111-1-11111-1-11-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-11-111-1-111-11
χ1211111111-1-1-1-1111-1-1-1-1111111-1-11111-1-11-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1111111-11-1-111-1-11-1
χ1311111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111111-1-1-111-1-1-11
χ1411111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-1-1111-1-1111-1
χ1511111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1111111111111-1-1-1-1111111-1-1-1-1111-1-1-1-1-1111-1
χ1611111111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-111111111-1-11111-1-1111111-1-1-1-1-1-1-111111-1-1-11
χ172222222222222222222-2-2-2-22-2-2-20000-2-2-2000000000000000022002200000000000000-2-200000000
χ182222222222222222222-2-2-2-22-2-2-20000-2-2-20000000000000000-2-200-2-2000000000000002200000000
χ19222222222222-2-2-2-2-2-2-22222-2-2-2-2222222-20000000000000000002200-2-2-2-200000000000000000000
χ20222222222222-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222-2000000000000000000-2-200222200000000000000000000
χ21222222222222-2-2-2-2-2-2-2-2-2-2-2-22220000-2-2200000000000000000000000000000000002-2002-2000000
χ22222222222222-2-2-2-2-2-2-2-2-2-2-2-22220000-2-220000000000000000000000000000000000-2200-22000000
χ2322222222-2-2-2-2222-2-2-2-2-2-2-2-22-222000022-200000000000000002200-2-200000000000000-2200000000
χ2422222222-2-2-2-2222-2-2-2-2-2-2-2-22-222000022-20000000000000000-2-20022000000000000002-200000000
χ2522222222-2-2-2-2-2-2-222222222-2-2222222-2-2-2000000000000000000-2-200-2-22200000000000000000000
χ2622222222-2-2-2-2-2-2-222222222-2-222-2-2-2-2-2-2-2000000000000000000220022-2-200000000000000000000
χ2722222222-2-2-2-2-2-2-22222-2-2-2-2-22-2-2000022200000000000000000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-22222-2-2-2-2-22-2-200002220000000000000000000000000000000000-22002-2000000
χ29222-2-2-2-2200000002i2i−2i−2i2-22-2002i−2i2i2i−2i−2i0002222−2−2−2−2i2i2i2i2−i2−i2−i2−i2000000002-2i2i2−i2−i222−2−2000000000000
χ30222-2-2-2-2200000002i2i−2i−2i2-22-2002i−2i2i2i−2i−2i000−2−2−2−22222−i2−i2−i2−i2i2i2i2i2000000002-2−i2−i2i2i2−2−222000000000000
χ31222-2-2-2-2200000002i2i−2i−2i2-22-2002i−2i−2i−2i2i2i0002222−2−2−2−2i2i2i2i2−i2−i2−i2−i200000000-22−i2−i2i2i2−2−222000000000000
χ32222-2-2-2-2200000002i2i−2i−2i2-22-2002i−2i−2i−2i2i2i000−2−2−2−22222−i2−i2−i2−i2i2i2i2i200000000-22i2i2−i2−i222−2−2000000000000
χ33222-2-2-2-220000000−2i−2i2i2i2-22-200−2i2i2i2i−2i−2i0002222−2−2−2−2−i2−i2−i2−i2i2i2i2i200000000-22i2i2−i2−i2−2−222000000000000
χ34222-2-2-2-220000000−2i−2i2i2i2-22-200−2i2i2i2i−2i−2i000−2−2−2−22222i2i2i2i2−i2−i2−i2−i200000000-22−i2−i2i2i222−2−2000000000000
χ35222-2-2-2-220000000−2i−2i2i2i2-22-200−2i2i−2i−2i2i2i0002222−2−2−2−2−i2−i2−i2−i2i2i2i2i2000000002-2−i2−i2i2i222−2−2000000000000
χ36222-2-2-2-220000000−2i−2i2i2i2-22-200−2i2i−2i−2i2i2i000−2−2−2−22222i2i2i2i2−i2−i2−i2−i2000000002-2i2i2−i2−i2−2−222000000000000
χ3722-222-2-2-222-2-22-2-22-22-2000020000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i22i−2i002i−2i0000000000000000002−22−200
χ3822-222-2-2-222-2-22-2-22-22-2000020000000000i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2−2i2i00−2i2i000000000000000000−22−2200
χ3922-222-2-2-222-2-22-2-22-22-2000020000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i22i−2i002i−2i000000000000000000−22−2200
χ4022-222-2-2-222-2-22-2-22-22-2000020000000000−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−2i2i00−2i2i0000000000000000002−22−200
χ4122-222-2-2-2-2-2222-2-2-22-22000020000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i22i−2i00−2i2i0000000000000000002−2−2200
χ4222-222-2-2-2-2-2222-2-2-22-22000020000000000i2i2−i2−i2i2i2−i2−i2−i2−i2i2i2−i2−i2i2i2−2i2i002i−2i000000000000000000−222−200
χ4322-222-2-2-2-2-2222-2-2-22-22000020000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i22i−2i00−2i2i000000000000000000−222−200
χ4422-222-2-2-2-2-2222-2-2-22-22000020000000000−i2−i2i2i2−i2−i2i2i2i2i2−i2−i2i2i2−i2−i2−2i2i002i−2i0000000000000000002−2−2200
χ452-2-22-22-222-22-2000000022-2-200002i−2i2i−2i2-202−22−22−22−22−22−22−22−2002i−2i000000i2−i2i2−i2i2−i2i2−i2000000000000
χ462-2-22-22-222-22-2000000022-2-200002i−2i2i−2i2-20−22−22−22−22−22−22−22−22002i−2i000000−i2i2−i2i2−i2i2−i2i2000000000000
χ472-2-22-22-222-22-2000000022-2-20000−2i2i−2i2i2-202−22−22−22−22−22−22−22−200−2i2i000000−i2i2−i2i2−i2i2−i2i2000000000000
χ482-2-22-22-222-22-2000000022-2-20000−2i2i−2i2i2-20−22−22−22−22−22−22−22−2200−2i2i000000i2−i2i2−i2i2−i2i2−i2000000000000
χ492-2-22-22-22-22-22000000022-2-200002i−2i2i−2i-2202−22−22−22−2−22−22−22−2200−2i2i000000i2−i2i2−i2−i2i2−i2i2000000000000
χ502-2-22-22-22-22-22000000022-2-200002i−2i2i−2i-220−22−22−22−222−22−22−22−200−2i2i000000−i2i2−i2i2i2−i2i2−i2000000000000
χ512-2-22-22-22-22-22000000022-2-20000−2i2i−2i2i-2202−22−22−22−2−22−22−22−22002i−2i000000−i2i2−i2i2i2−i2i2−i2000000000000
χ522-2-22-22-22-22-22000000022-2-20000−2i2i−2i2i-220−22−22−22−222−22−22−22−2002i−2i000000i2−i2i2−i2−i2i2−i2i2000000000000
χ532-2-2-22-222000022-200002-2-22-22002-2-2200-2000000002i−2i2i−2i−2i2i−2i2i0000002-2000000−2i2i2i−2i000000000000
χ542-2-2-22-222000022-200002-2-22-22002-2-2200-200000000−2i2i−2i2i2i−2i2i−2i0000002-20000002i−2i−2i2i000000000000
χ552-2-2-22-222000022-200002-2-22-2200-222-200-2000000002i−2i2i−2i−2i2i−2i2i000000-220000002i−2i−2i2i000000000000
χ562-2-2-22-222000022-200002-2-22-2200-222-200-200000000−2i2i−2i2i2i−2i2i−2i000000-22000000−2i2i2i−2i000000000000
χ572-2-2-22-2220000-2-2200002-2-222-2002-2-220022-22-2-22-2200000000000000-22002-2-220000000000000000
χ582-2-2-22-2220000-2-2200002-2-222-2002-2-22002-22-222-22-200000000000000-2200-222-20000000000000000
χ592-2-2-22-2220000-2-2200002-2-222-200-222-20022-22-2-22-22000000000000002-200-222-20000000000000000
χ602-2-2-22-2220000-2-2200002-2-222-200-222-2002-22-222-22-2000000000000002-2002-2-220000000000000000
χ61444-4-4-4-4400000004i4i−4i−4i-44-4400−4i4i00000000000000000000000000000000000000000000000000000
χ62444-4-4-4-440000000−4i−4i4i4i-44-44004i−4i00000000000000000000000000000000000000000000000000000
χ6344-444-4-4-444-4-4-444-44-440000-400000000000000000000000000000000000000000000000000000000
χ6444-444-4-4-4-4-444-4444-44-40000-400000000000000000000000000000000000000000000000000000000
χ6544-4-4-444-400000004i−4i−4i4i0000000000000002i2i−2i−2i−2i−2i2i2i-2-22222-2-2000000000000000000000000000000
χ6644-4-4-444-400000004i−4i−4i4i000000000000000−2i−2i2i2i2i2i−2i−2i22-2-2-2-222000000000000000000000000000000
χ6744-4-4-444-40000000−4i4i4i−4i0000000000000002i2i−2i−2i−2i−2i2i2i22-2-2-2-222000000000000000000000000000000
χ6844-4-4-444-40000000−4i4i4i−4i000000000000000−2i−2i2i2i2i2i−2i−2i-2-22222-2-2000000000000000000000000000000
χ694-444-4-44-44-4-4400000000000000000000002i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ704-444-4-44-44-4-440000000000000000000000−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ714-444-4-44-4-444-400000000000000000000002i−2i−2i2i2i−2i−2i2i−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000
χ724-444-4-44-4-444-40000000000000000000000−2i2i2i−2i−2i2i2i−2i2i−2i−2i2i2i−2i−2i2i000000000000000000000000000000
χ734-44-444-4-400004-4400000000-400000000000000000022−22−2222−222222−22000000000000000000000000000000
χ744-44-444-4-400004-4400000000-4000000000000000000−222222−2222−22−2222000000000000000000000000000000
χ754-44-444-4-40000-44-400000000400000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000000000
χ764-44-444-4-40000-44-40000000040000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000000000
χ774-4-44-44-444-44-40000000-4-44400000000-4400000000000000000000000000000000000000000000000
χ784-4-44-44-44-44-440000000-4-444000000004-400000000000000000000000000000000000000000000000
χ794-4-4-44-444000044-40000-444-4-4-40000000040000000000000000000000000000000000000000000000
χ804-4-4-44-4440000-4-440000-444-44400000000-40000000000000000000000000000000000000000000000

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